## Quick Reference

A sound approach to integration defines the integral as the limit, in a certain sense, of a sum. That this can be evaluated, when *f* is continuous, by finding an antiderivative of *f*, is the result embodied in the so-called Fundamental Theorem of Calculus. It establishes that integration is the reverse process to differentiation:

Theorem

If *f* is continuous on [*a*, *b*] and *ϕ* is a function such that *ϕ*′(*x*)=*f*(*x*) for all *x* in [*a*, *b*], then

*Subjects:*
Mathematics.

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