integrals

A number, the limit of the sums computed in a process in which the domain of a function is divided into small subsets and a possibly nominal value of the function on each subset is multiplied by the measure of that subset, all these products then being summed.

“The integral of x\mapsto x^2 on [0,1] is \frac{1}{3}.”

A definite integral, a limit of sums.

Antiderivative

“The integral of x^2 is \frac{x^3}{3} plus a constant.”