You need a "floor" for your solid - I'm going to assume z=0.
You divide the solid into two parts - the first part, with y going from 0 to 1, has the z=1 plane on the top. The second part, with y going from 1 to 2, has the y+z=2 plane on the top. All of the cross sections are rectangles.
where I substituted length times width for the area in both cases. Of course, the total volume is .
Post again in this thread if you're still having trouble.