I am trying to integrate the following shaded area:

I am supposed to solve the problem two ways (by integrating with respect to both x and y). I was having trouble with this one, especially with integrating with respect to y. The integrals that I ended up with when integrating with respect to x are:

Integral from 0 to 2 of 6 - 3x + Integral from 0 to 2 of pi.

Can anyone help out with this? Sorry, I don't know how to use the math tags.