The antidifferentiation and indefinite integrals

In calculus, an "anti-derivative", antiderivative, primitive integral or indefinite integral of a function f is a function F whose derivative is equal to f, i.e., F ′ = f. The process of solving for antiderivatives is called antidifferentiation (or indefinite integration) and its opposite function is called differentiation, which is the process of finding a derivative. Antiderivatives are related to definite integrals through the fundamental theorem of calculus: the definite integral of a function over an interval is equal to the difference between the values of an antiderivative evaluated at the endpoints of the interval.

Antidifferentiation is the process of finding the set of all antiderivatives of a given function. The symbol denotes the operation of antidifferentiation

where f(x).