## Calculus: Early Transcendentals (2nd Edition)

If $f$ is an odd function, $\int_{-a}^{a} f(x) dx = 0$ because of symmetry. Exactly one half of the total area will be negative and another half will be positive, making the net area zero.
$\int_{-a}^{a} f(x) dx = \int_{-a}^0 f(x) dx + \int_0^a f(x) dx = -n + n = 0$, where $n$ is the value given when evaluating the integral.