Volume by Cross Section Verification

I had to make a model of the function y=sin(x) and then find the volume of that model.

Below is a picture of the model I made, and vertical cardboard sections were placed 1/2 an inch apart from each other so (pi/2) = 2.5 inches.

http://i40.tinypic.com/zn9e75.jpg

I know that I need to integrate the area formula of the cross section with the limits to find area in in^2.

The volume of each square cross section is (sin(x)^2), and the model goes from -pi to pi.

I'm pretty sure the indefinite integral of this is -cos^2(x), but

I don't know where to take this problem from here. When I did the math in my calculator, I got pi in^3 as the answer, but by no means am I positive.

Thanks, in advance for your help.