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.
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