Examples 7.1.11(c): Riemann Lemma
For an evenly spaced partition that includes 0 it is easy to compute a particular Riemann sum (such as a "middle Riemann sum") as long as the function is odd.
The rest is left as an exercise.
For even functions, i.e. functions where f(x) = f(-x), we can show that the integral of f from -a to a is twice the integral from 0 to a. The details are left as an exercise again (sorry -:).