ABSTRACT
Antiderivative and Indenite Integral. A function f (x) is integrable on a set S if there exists a dierentiable on S function F (x) such that F 0 (x) = f (x) for 8x 2 S. The function F (x) is called an antiderivative (or a primitive) of the function f (x) on S. If F (x) is an antiderivative of f (x) on S, then the set of all antiderivatives is called an indenite integral of f (x) on S and it has the form F (x) + C, where C is an arbitrary real constant. The standard notation is F (x) + C =
R f (x) dx.
