What word or phrase does your mother always say?
1630s, "to render (something) whole," from Latin integratus, past participle of integrare "make whole," from integer "whole" (see integer). Meaning "to put together parts or elements and combine them into a whole" is from 1802. Integrate in the "racially desegregate" sense is a back-formation from integration, dating to the 1948 U.S. presidential contest. Related: Integrated; integrating.