antiderivative

A function whose derivative is the given function. If `F'(x) = f(x)`, then `F` is _an_ antiderivative of `f` — there are infinitely many, all differing by a constant: `F(x) + C` is also an antiderivative for any constant `C`. The antiderivative is what differentiation _undoes_; the fundamental theorem of calculus says it's also what the definite integral _computes_: `∫_a^b f(x) dx = F(b) − F(a)`. The constant `C` cancels because the integral subtracts two values of `F`. Often called _indefinite integral_ in textbooks (notation `∫ f(x) dx`), but "antiderivative" names the _function itself_ more precisely; "indefinite integral" emphasizes the operation.