If F(x) is a derivable function, we know how to calculate its derivative f(x)=F '(x).

Is it possible to put the reverse problem? For a given function f(x), does a function F(x), derivative of wich equals f(x), exist?

If it exists, we will call it primitive of the given function f(x).

If F(x) is a primitive of f(x), all the functions F(x)+k are primitives of f(x), since derivative of a constant k is zero.

By definition we call Indefinite Integral  of the function f(x) the whole of its primitives.