Integration of an even power, various limits:

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

Let's confirm this:

This confirms that . This is generally true for symmetric limits and and even function.