Techniques of Integration · Hard problem

A circular submarine viewport of radius $2$ ft is mounted vertically with its center $5$ ft below the surface. Using weight density $62.5$ lb/ft$^3$, the hydrostatic force on it is $F=\displaystyle\int_{-2}^{2}62.5(5-y)\cdot2\sqrt{4-y^2}\,dy$, where $y$ is measured from the viewport's center. Find $F$ (in lb).