Integrate
mid 17th century: from Latin integrat- ‘made whole’, from the verb integrare, from integer ‘whole’ (see integer). Compare with integral and integrity.
wiktionary
Borrowed from Latin integrātus, perfect participle of integrō(“I make whole, I renew, I repair, I begin again”), from integer(“whole, fresh”); see integer, integral.
etymonline
integrate (v.)
1630s, "to render (something) whole, bring together the parts of," from Latin integratus, past participle of integrare "make whole," from integer "whole, complete," figuratively, "untainted, upright," literally "untouched," from in- "not" (see in- (1)) + root of tangere "to touch," from PIE root *tag- "to touch, handle."
The meaning "put together parts or elements and combine them into a whole" is from 1802. The "racially desegregate" sense (1940) probably is a back-formation from integration. Related: Integrated; integrating.