i'll give the problem then explain my issue with it.

the solid lies between planes perpendicular to the x axis at x=-1 and x=1. The cross sections perp. to the x axis are circular disks whose diameters run from the parabola y=x^2 to the parabola y=2-x^2

seems pretty simple but for the life of me i can't figure it out. I figured to use the washer method, with y=2-x^2 being R and y=x^2 being r. so i set that up and integrate it, and get volume = pi(4x-2x^2/3) . (There were two other functions, but one was positive, one was negative, so they cancel out, leaving this). I need to evaulate that from -1 to 1. but doing that results in 0, which obviously can't be the answer. where did i go wrong?