With calculus it became possible to get

*exact* answers for these problems with almost no effort, because in the limit these sums became definite integrals and definite integrals could be evaluated with antiderivatives. With calculus, the challenge became one of finding an antiderivative for it. In this chapter you will do precisely that, find areas between irregular curves and volumes of irregular solids. (Taken from an excerpt in the fifth edition of the Finney, Demana, Waits, Kennedy, and Bressoud textbook

*Calculus - Graphical, Numerical, Algebraic*.)