Optimization or area under parabola

This question isn't really optimization but the second part is (which I know how to do). Its the first part i'm stuck at.

The cross-section of a building constructed inside a parabolic framework is shown in the diagram.

http://img259.imageshack.us/img259/3051/sketchgx8.jpg

(sorry for bad drawing)

a) Given that PQ is 2*x*m show that the shaded area is **6x - 2x^3**

The only thing I can think of is to multiply the equation of the parabola

(3 - x^2) by 2x, which gives 6x - 2x^3 .

Can you tell how the proper way to do it is?

Thanks