before I look up integritous, let me just opine that it's just hokey enough to have been used in C. 17 or 18 -- you know, one of those inkhorn terms. :)

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well, the inkhorners seem to have gone in a slightly different direction:

integrious [a.] - Obs. rare. Marked by integrity. Hence †in"tegriously adv.
1658 Sir H. Slingsby Diary (1836) 201 Such was their integrious candor and intimacy to me in my greatest extremes. Ibid. 208 Being so integriously grounded, as it admitted no alloy or mixture with By-respects or self-interests.

integritive [a.] - Obs. rare. Marked by integrity; upright, sincere.
1784 Burns Comm.-pl. Bk. Aug., To maintain an integritive conduct towards our fellow-creatures.