A volume is described as follows:

1. The base is the region bounded by $\displaystyle x= -y^{2} + 8y + 21 $ and $\displaystyle x=y^{2} - 18y + 93 $;

2. Every cross section perpendicular to they-axis is a semi-circle.

Find the volume.

So you would find the area by doing:

$\displaystyle \int_4^{9}(-y^{2} +8y + 21 -( y^{2} -18y + 93))dy$

Right? But then i don't understand how you would find the volume....