It was widely used by Ramanujan to calculate definite integrals and infinite series.

Functionals are often expressed as definite integrals involving functions and their derivatives.

More precisely, it relates the values of antiderivatives to definite integrals.

Mathematicians have used definite integrals as a tool to define identities.

Earlier systems such as Macsyma had a few definite integrals related to special functions within a look-up table.

Derivatives and definite integrals are evaluated exactly when possible, and approximately otherwise.

In 1950, the second volume containing definite integrals appeared.

A major open question is whether sufficiently well behaved surreal functions possess definite integrals.

Another difference is in the placement of limits for definite integrals.

Cauchy early undertook the general theory of determining definite integrals, and the subject has been prominent during the 19th century.