Yes, your graph is fine.
To integrate over the x-axis, you need
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