Integration is the reverse of what mathematical operation?

The story behind the answer

Integration is the reverse (inverse) of derivation, also called differentiation. Differentiation gives the rate of change: if F(x) models position, F′(x) is velocity. Integration undoes this by accumulating those rates back to the original quantity: if F′(x) = f(x), then the integral of f(x) is F(x) + C. This link is formalized by the Fundamental Theorem of Calculus, which bridges derivatives and integrals.

A memory tip: differentiate to get “details” (instantaneous change), integrate to “integrate” pieces into a whole (total change/area). Think of ∫ as a summing machine and d/dx as a differencing machine—one builds up, the other breaks down.