Integral Acquisition Corporation 1 New York, New York 10065

Exhibit 10.1

[•], 2021

Integral Acquisition Corporation 1

▇▇▇ ▇▇▇▇▇▇▇ ▇▇▇▇▇▇

New York, New York 10065

Re: Initial Public Offering

Ladies and Gentlemen:

This letter (this “Letter Agreement”) is being delivered to you in accordance with the Underwriting Agreement (the “Underwriting Agreement”) entered into by and among Integral Acquisition Corporation 1, a Delaware corporation (the “Company”), and ▇▇▇▇▇ Fargo Securities, LLC, as representative (the “Representative”) of the underwriters (each, an “Underwriter” and collectively, the “Underwriters”), relating to an underwritten initial public offering (the “Public Offering”), of up to 11,500,000 of the Company’s units (including up to 1,500,000 units that may be purchased to cover over-allotments, if any) (the “Units”), each comprised of one share of the Company’s Class A common stock, par value $0.0001 per share (the “Class A Common Stock”), and one half of one redeemable warrant. Each whole warrant (each, a “Warrant”) entitles the holder thereof to purchase one share of Class A Common Stock at a price of $11.50 per share, subject to adjustment as described in the Prospectus (as defined below). The Units will be sold in the Public Offering pursuant to a registration statement on Form S-1 and prospectus (the “Prospectus”) filed by the Company with the U.S. Securities and Exchange Commission (the “Commission”) and the Company has applied to have the Units listed on The Nasdaq Capital Market. Certain capitalized terms used herein are defined in paragraph 11 hereof.

In order to induce the Company and the Underwriters to enter into the Underwriting Agreement and to proceed with the Public Offering and for other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, each of Integral Sponsor LLC (the “Sponsor”) and the undersigned individuals, each of whom is a member of the Company’s board of directors and/or management team (each of the undersigned individuals, an “Insider” and collectively, the “Insiders”), ▇▇▇▇▇▇ agrees with the Company as follows:

1. The Sponsor and each Insider agree that if the Company seeks stockholder approval of a proposed Business Combination, then in connection with such proposed Business Combination, it, he or she shall (i) vote any shares of Common Stock (as defined below) owned by it, him or her in favor of any proposed Business Combination and (ii) not redeem any shares of Common Stock owned by it, him or her in connection with such stockholder approval. If the Company seeks to consummate a proposed Business Combination by engaging in a tender offer, the Sponsor and each Insider agree that it, he or she will not sell or tender any shares of Common Stock owned by it, him or her in connection therewith.

2. The Sponsor and each Insider hereby agree that in the event that the Company fails to consummate a Business Combination within 18 months after the closing of the Public Offering, or such later period approved by the Company’s stockholders in accordance with the Company’s amended and restated certificate of incorporation (as it may be amended from time to time, the “Charter”), the Sponsor and each Insider shall take all reasonable steps to cause the Company to (i) cease all operations except for the purpose of winding up, (ii) as promptly as reasonably possible but not more than ten business days thereafter, redeem 100% of the shares of Class A Common Stock sold as part of the Units in the Public Offering (the “Offering Shares”), at a per-share price, payable in cash, equal to the aggregate amount then on deposit in the Trust Account (as defined below), including interest earned on the funds held in the Trust Account (which interest shall be net of taxes payable and less up to $100,000 of interest to pay dissolution expenses), divided by the number of then outstanding Offering Shares, which redemption will completely extinguish all Public Stockholders’ (as defined below) rights as stockholders (including the right to receive further liquidating distributions, if any), and (iii) as promptly as reasonably possible following such redemption, subject to the approval of the Company’s remaining stockholders and the Company’s board of directors, liquidate and dissolve, subject in each case to the Company’s obligations under Delaware law to provide for claims of creditors and other requirements of applicable law. The Sponsor and each Insider agree to not propose any amendment to the Charter to modify the substance or timing of the Company’s obligation to redeem 100% of the

Offering Shares if the Company does not complete a Business Combination within the required time period set forth in the Charter or with respect to any other material provisions relating to stockholders’ rights or pre-initial business combination activity, unless the Company provides its Public Stockholders with the opportunity to redeem their Offering Shares upon approval of any such amendment at a per-share price, payable in cash, equal to the aggregate amount then on deposit in the Trust Account, including interest earned on the funds held in the Trust Account and not previously released to the Company to pay its taxes, divided by the number of then outstanding Offering Shares.

The Sponsor and each Insider acknowledge that it, he or she has no right, title, interest or claim of any kind in or to any monies held in the Trust Account or any other asset of the Company as a result of any liquidation of the Company with respect to the Founder Shares held by it, him or her. The Sponsor and each Insider hereby further waive, with respect to any shares of Common Stock held by it, him or her, if any, any redemption rights it, he or she may have in connection with (A) the consummation of a Business Combination, including, without limitation, any such rights available in the context of a stockholder vote to approve such Business Combination, or (B) a stockholder vote to approve an amendment to the Charter to modify the substance or timing of the Company’s obligation to redeem 100% of the Offering Shares if the Company has not consummated a Business Combination within the time period set forth in the Charter or with respect to any other material provisions relating to stockholders’ rights or pre-initial business combination activity or in the context of a tender offer made by the Company to purchase Offering Shares (although the Sponsor, the Insiders and their respective affiliates shall be entitled to redemption and liquidation rights with respect to any Offering Shares it or they hold if the Company fails to consummate a Business Combination within the time period set forth in the Charter).

3. During the period commencing on the effective date of the Underwriting Agreement and ending 180 days after such date, the Sponsor and each Insider shall not, without the prior written consent of the Representatives, (i) sell, offer to sell, contract or agree to sell, hypothecate, pledge, grant any option to purchase or otherwise dispose of or agree to dispose of, directly or indirectly, or establish or increase a put equivalent position or liquidate or decrease a call equivalent position within the meaning of Section 16 of the Securities Exchange Act of 1934, as amended (the “Exchange Act”), and the rules and regulations of the Commission promulgated thereunder, with respect to, any Units, shares of Common Stock (including, but not limited to, Founder Shares), Warrants or any securities convertible into, or exercisable or exchangeable for, shares of Common Stock owned by it, him or her, (ii) enter into any swap or other arrangement that transfers to another, in whole or in part, any of the economic consequences of ownership of any Units, shares of Common Stock (including, but not limited to, Founder Shares), Warrants or any securities convertible into, or exercisable or exchangeable for, shares of Common Stock owned by it, him or her, whether any such transaction is to be settled by delivery of such securities, in cash or otherwise, or (iii) publicly announce any intention to effect any transaction specified in clause (i) or (ii).

4. In the event of the liquidation of the Trust Account upon the failure of the Company to consummate its initial Business Combination within the time period set forth in the Charter, the Sponsor (the “Indemnitor”) agrees to indemnify and hold harmless the Company against any and all loss, liability, claim, damage and expense whatsoever (including, but not limited to, any and all legal or other expenses reasonably incurred in investigating, preparing or defending against any litigation, whether pending or threatened) to which the Company may become subject as a result of any claim by (i) any third party for services rendered or products sold to the Company or (ii) any prospective target business with which the Company has entered into a written letter of intent, confidentiality or other similar agreement or Business Combination agreement (a “Target”); provided, however, that such indemnification of the Company by the Indemnitor (x) shall apply only to the extent necessary to ensure that such claims by a third party or a Target do not reduce the amount of funds in the Trust Account to below the lesser of (i) $10.15 per Offering Share and (ii) the actual amount per Offering Share held in the Trust Account as of the date of the liquidation of the Trust Account, if less than $10.15 per Offering Share is then held in the Trust Account due to reductions in the value of the trust assets, less taxes payable, (y) shall not apply to any claims by a third party or a Target that executed a waiver of any and all rights to the monies held in the Trust Account (whether or not such waiver is enforceable) and (z) shall not apply to any claims under the Company’s indemnity of the Underwriters against certain liabilities, including liabilities under the Securities Act of 1933, as amended. The Indemnitor shall have the right to defend against any such claim with counsel of its choice reasonably satisfactory to the Company if, within 15 days following written receipt of notice of the claim to the Indemnitor, the Indemnitor notifies the Company in writing that it shall undertake such defense.

5. To the extent that the Underwriters do not exercise their over-allotment option to purchase up to an additional 1,500,000 Units within 45 days after the date of the Prospectus (and as further described in the Prospectus), the Sponsor agrees to forfeit, at no cost, a number of Founder Shares in the aggregate equal to 375,000 multiplied by a fraction, (i) the numerator of which is 1,500,000 minus the number of Units purchased by the Underwriters upon the exercise of their over-allotment option, and (ii) the denominator of which is 1,500,000. The forfeiture will be adjusted to the extent that the over-allotment option is not exercised in full by the Underwriters so that the Founder Shares will represent an aggregate of 20.0% of the Company’s issued and outstanding shares of Class A Common Stock after the Public Offering (not including shares of Class A Common Stock underlying the Warrants or Private Placement Warrants (as defined below)). The Sponsor further agrees that to the extent that the size of the Public Offering is increased or decreased, the Company will purchase or sell Units or effect a share repurchase or share capitalization, as applicable, immediately prior to the consummation of the Public Offering in such amount as to maintain the ownership of the initial shareholders prior to the Public Offering at 20.0% of its issued and outstanding shares of Class A Common Stock upon the consummation of the Public Offering (not including shares of Class A Common Stock underlying the Warrants or Private Placement Warrants). In connection with such increase or decrease in the size of the Public Offering, then (A) the references to 1,500,000 in the numerator and denominator of the formula in the first sentence of this paragraph shall be changed to a number equal to 15% of the number of Public Shares included in the Units issued in the Public Offering and (B) the reference to 375,000 in the formula set forth in the first sentence of this paragraph shall be adjusted to such number of Founder Shares that the Sponsor would have to surrender to the Company in order for the initial shareholders to hold an aggregate of 20.0% of the Company’s issued and outstanding shares of Class A Common Stock after the Public Offering (not including shares of Class A Common Stock underlying the Warrants or Private Placement Warrants).

6. The Sponsor and each Insider hereby agree and acknowledge that: (i) the Underwriters and the Company would be irreparably injured in the event of a breach by such Sponsor or an Insider of its, his or her obligations under paragraphs 1, 2, 3, 4, 5, 7(a), and 7(b), as applicable, of this Letter Agreement (ii) monetary damages may not be an adequate remedy for such breach and (iii) the non-breaching party shall be entitled to injunctive relief, in addition to any other remedy that such party may have in law or in equity, in the event of such breach.

7. (a) The Sponsor and each Insider agree that it, he or she shall not Transfer any Founder Shares (or any shares of Class A Common Stock issuable upon conversion thereof) until the earlier of (A) one year after the completion of the Company’s initial Business Combination and (B) subsequent to the Business Combination, (x) if the closing price of the Class A Common Stock equals or exceeds $12.00 per share (as adjusted for stock splits, stock dividends, reorganizations, recapitalizations and the like) for any 20 trading days within any 30-trading day period commencing at least 150 days after the Company’s initial Business Combination or (y) the date on which the Company completes a liquidation, merger, capital stock exchange, reorganization or other similar transaction that results in all of the Company’s stockholders having the right to exchange their shares of Class A Common Stock for cash, securities or other property (the “Founder Shares Lock-up Period”).

(b) The Sponsor and each Insider agree that it, he or she shall not Transfer any Private Placement Warrants (or any share of Class A Common Stock issued or issuable upon the exercise of the Private Placement Warrants), until 30 days after the completion of a Business Combination (the “Private Placement Warrants Lock-up Period”, together with the Founder Shares Lock-up Period, the “Lock-up Periods”).

(c) Notwithstanding the provisions set forth in paragraphs 7(a) and (b), Transfers of the Founder Shares, Private Placement Warrants and shares of Class A Common Stock issued or issuable upon the exercise or conversion of the Private Placement Warrants or the Founder Shares that are held by the Sponsor, any Insider or any of their permitted transferees (that have complied with this paragraph 7(c)), are permitted (a) to the Company’s officers or directors, any affiliate or family member of any of the Company’s officers or directors, any affiliate of the Sponsor or to any members of the Sponsor or any of their affiliates; (b) in the case of an individual, by gift to a member of such individual’s immediate family or to a trust, the beneficiary of which is a member of such individual’s immediate family, an affiliate of such individual or to a charitable organization; (c) in the case of an individual, by virtue of laws of descent and distribution upon death of such individual; (d) in the case of an individual, pursuant to a qualified domestic relations order; (e) by private sales or transfers made in connection with any forward purchase agreement or similar arrangement or in connection with the consummation of an initial Business Combination at prices no greater than the price at which the securities were originally purchased; (f) in the

event of the Company’s liquidation prior to the completion of an initial Business Combination; (g) by virtue of the laws of the State of Delaware or the Sponsor’s limited liability company agreement upon dissolution of the Sponsor; or (h) in the event of the Company’s liquidation, merger, capital stock exchange or other similar transaction that results in all of the Company’s stockholders having the right to exchange their shares of Class A Common Stock for cash, securities or other property subsequent to the Company’s completion of an initial Business Combination; provided, however, that in the case of clauses (a) through (e) or (g), these permitted transferees must enter into a written agreement with the Company agreeing to be bound by the transfer restrictions herein and the other restrictions contained in this Agreement (including provisions relating to voting, the Trust Account and liquidating distributions).

8. The Sponsor and each Insider represents and warrants that it, he or she has never been suspended or expelled from membership in any securities or commodities exchange or association or had a securities or commodities license or registration denied, suspended or revoked. Each Insider’s biographical information furnished to the Company (including any such information included in the Prospectus) is true and accurate in all respects and does not omit any material information with respect to the Insider’s background. The Sponsor and each Insider’s questionnaire furnished to the Company is true and accurate in all respects. The Sponsor and each Insider represents and warrants that: it, he or she is not subject to or a respondent in any legal action for, any injunction, cease-and-desist order or order or stipulation to desist or refrain from any act or practice relating to the offering of securities in any jurisdiction; it, he or she has never been convicted of, or pleaded guilty to, any crime (i) involving fraud, (ii) relating to any financial transaction or handling of funds of another person, or (iii) pertaining to any dealings in any securities and it, he or she is not currently a defendant in any such criminal proceeding.

9. Except as disclosed in the Prospectus, neither the Sponsor nor any officer, nor any affiliate of the Sponsor or any officer, nor any director of the Company, shall receive from the Company any finder’s fee, reimbursement, consulting fee, non-cash payments, monies in respect of any repayment of a loan or other compensation prior to, or in connection with any services rendered in order to effectuate, the consummation of the Company’s initial Business Combination (regardless of the type of transaction that it is), other than the following, none of which will be made from the proceeds held in the Trust Account prior to the completion of the initial Business Combination: repayment of a loan and advances up to an aggregate of $300,000 made to the Company by the Sponsor; payments to the Sponsor for certain office space, secretarial and administrative services as may be reasonably required by the Company of $20,000 per month; reimbursement for any reasonable out-of-pocket expenses related to identifying, investigating, negotiating and completing an initial Business Combination, and repayment of loans, if any, and on such terms as to be determined by the Company from time to time, made by the Sponsor or an affiliate of the Sponsor or any of the Company’s officers or directors to finance transaction costs in connection with an intended initial Business Combination, provided, that, if the Company does not consummate an initial Business Combination, a portion of the working capital held outside the Trust Account may be used by the Company to repay such loaned amounts so long as no proceeds from the Trust Account are used for such repayment. Up to $1,500,000 of such loans may be convertible into warrants at a price of $1.00 per warrant at the option of the lender. Such warrants would be identical to the Private Placement Warrants, including as to exercise price, exercisability and exercise period.

10. The Sponsor and each Insider has full right and power, without violating any agreement to which it is bound (including, without limitation, any non-competition or non-solicitation agreement with any employer or former employer), to enter into this Letter Agreement and, as applicable, to serve as an officer and/or director on the board of directors of the Company and hereby consents to being named in the Prospectus as an officer and/or director of the Company.

11. As used herein, (i) “Business Combination” shall mean a merger, capital stock exchange, asset acquisition, stock purchase, reorganization or similar business combination, involving the Company and one or more businesses; (ii) “Common Stock” shall mean the Class A common stock and Class B common stock; (iii) “Founder Shares” shall mean the 2,875,000 shares of Class B common stock issued and outstanding (up to 375,000 Shares of which are subject to complete or partial forfeiture if the over-allotment option is not exercised by the Underwriters); (iv) “Initial Stockholders” shall mean the Sponsor and any Insider that holds Founder Shares; (v) “Private Placement Warrants” shall mean the 4,860,000 Warrants (or, if the underwriters’ over-allotment option is exercised, up to 4,950,000 Warrants) that the Sponsor has agreed to purchase for an aggregate purchase price of $4,860,000 (or, if the underwriters’ over-allotment option is exercised up to $4,950,000), or $1.00 per Warrant, in a private placement that shall occur simultaneously with the consummation of the Public Offering; (vi) “Public Stockholders” shall mean the holders of securities issued in the

Public Offering; (vii) “Trust Account” shall mean the trust fund into which a portion of the net proceeds of the Public Offering and the sale of the Private Placement Warrants shall be deposited; (viii) “Transfer” shall mean the (a) sale of, offer to sell, contract or agreement to sell, hypothecate, pledge, grant of any option to purchase or otherwise dispose of or agreement to dispose of, directly or indirectly, or establishment or increase of a put equivalent position or liquidation with respect to or decrease of a call equivalent position within the meaning of Section 16 of the Exchange Act, and the rules and regulations of the Commission promulgated thereunder with respect to, any security, (b) entry into any swap or other arrangement that transfers to another, in whole or in part, any of the economic consequences of ownership of any security, whether any such transaction is to be settled by delivery of such securities, in cash or otherwise, or (c) public announcement of any intention to effect any transaction specified in clause (a) or (b); and (ix) “Warrants” shall mean the Private Placement Warrants and public warrants.

12. The Company will maintain an insurance policy or policies providing directors’ and officers’ liability insurance, and each Director shall be covered by such policy or policies, in accordance with its or their terms, to the maximum extent of the coverage available for any of the Company’s directors or officers.

13. This Letter Agreement constitutes the entire agreement and understanding of the parties hereto in respect of the subject matter hereof and supersedes all prior understandings, agreements, or representations by or among the parties hereto, written or oral, to the extent they relate in any way to the subject matter hereof or the transactions contemplated hereby. This Letter Agreement may not be changed, amended, modified or waived (other than to correct a typographical error) as to any particular provision, except by a written instrument executed by all parties hereto.

14. No party hereto may assign either this Letter Agreement or any of its rights, interests, or obligations hereunder without the prior written consent of the other parties. Any purported assignment in violation of this paragraph shall be void and ineffectual and shall not operate to transfer or assign any interest or title to the purported assignee. This Letter Agreement shall be binding on the Sponsor and each Insider and their respective successors, heirs and assigns and permitted transferees.

15. Nothing in this Letter Agreement shall be construed to confer upon, or give to, any person or corporation other than the parties hereto any right, remedy or claim under or by reason of this Letter Agreement or of any covenant, condition, stipulation, promise or agreement hereof. All covenants, conditions, stipulations, promises and agreements contained in this Letter Agreement shall be for the sole and exclusive benefit of the parties hereto and their successors, heirs, personal representatives and assigns and permitted transferees.

16. This Letter Agreement may be executed in any number of original or facsimile counterparts and each of such counterparts shall for all purposes be deemed to be an original, and all such counterparts shall together constitute but one and the same instrument.

17. This Letter Agreement shall be deemed severable, and the invalidity or unenforceability of any term or provision hereof shall not affect the validity or enforceability of this Letter Agreement or of any other term or provision hereof. Furthermore, in lieu of any such invalid or unenforceable term or provision, the parties hereto intend that there shall be added as a part of this Letter Agreement a provision as similar in terms to such invalid or unenforceable provision as may be possible and be valid and enforceable.

18. This Letter Agreement and all matters arising therefrom or relating thereto shall be governed by and construed and enforced in accordance with the laws of the State of New York. The parties hereto (i) all agree that any action, proceeding, claim or dispute arising out of, or relating in any way to, this Letter Agreement shall be brought and enforced in the courts of New York City, in the State of New York, and irrevocably submit to such jurisdiction and venue, which jurisdiction and venue shall be exclusive and (ii) waive any objection to such exclusive jurisdiction and venue or that such courts represent an inconvenient forum.

19. Any notice, consent or request to be given in connection with any of the terms or provisions of this Letter Agreement shall be in writing and shall be sent by express mail or similar private courier service, by certified mail (return receipt requested), by hand delivery or facsimile transmission.

20. This Letter Agreement shall terminate on the earlier of (i) the expiration of the Lock-up Periods or (ii) the liquidation of the Company; provided, however, that this Letter Agreement shall earlier terminate in the event that the Public Offering is not consummated and closed by December 31, 2021; provided further that paragraph 4 of this Letter Agreement shall survive such liquidation.

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