\section*{Introduction}

In this module, you will continue the discussion of integrals that
began in Module 4 and further synthesize the seemingly unrelated
problems of finding the area under a curve and determining
information about the (change in) values of an antiderivative using
the derivative.  You will meet the {\bf definite integral}, a notion
that you have already seen how to approximate and compute in many
instances, and how the two different objects called `integrals' are
related.  Later, you will meet better techniques for approximating
areas under curves, and will sew how the computations you have
learned can be stretched to solve other problems.

This is the second of the two theory modules.  In these modules, we
will excuse ourselves from the applications in order to develop
technical skills.  In particular, after completing this module, you
will be able to compute areas under curves exactly for a number of
functions without directly using limits.

