Integration of an odd power, various limits:

By the symmetry of the graph, we see that the area under the curve between -2 and 0 is the negative of that between 0 and 2. Consequently, the area (and integral) from -2 to 2 is 0. Note that this reasoning depends only on the fact that this is an odd function.

Let's confirm this:

This confirms that the integral between symmetrical limits of an odd function is zero.