Yes, your graph is fine.

To integrate over the x-axis, you need

so

Take the positive one and double your result as the x-axis is an axis of symmetry.

To integrate over the y-axis, you could integrate from to

If you like, again use the x-axis as an axis of symmetry and double the integral from to

This integral includes the unshaded part against the y-axis, so you have a few ways to cope with that.

The easiest way is to subtract 5 from

The new function is

so the limits of integration become

You can then calculate