why are integrals called anti derivatives rather than inverse derivatives

Question

If the integral of a derivative of a function produces the original function (within a constant), why are integrals referred to as anti derivatives rather than inverse derivatives?

Answer 1

Well, "anti-" means the same as "inverse" (i.e., opposite to), so I guess it is just a matter of choice and tradition. For me, at least, the word "antiderivative" sounds better, but maybe it's just what I'm used to.

Answer 2

Inverse functions are unique, whereas antiderivates are actually infinite (one for every choice of the integration constant.)