y=x^2-12 is a parabola pointing upwards with vertex at (0,-12) while the other is a parabola pointing downwards with vertex at (0,20). both of them meet at(+-4,4).

Now integrating along the x-axis will lead to complications. better will be to integrate along y-axis.then the integral will be from 20 to -12and the expression will be as in the attachment.