Actually the antiderivative of 1/(1 + x^2) is arctan(x), and you MUST use the brackets where they are needed.
Have you tried sketching the region to start with?
Find the volume of the solid obtained by rotating the region R bounded by the curves
y = 1/1+x^2, y=0,x=0 and x=2 about the x axis.
I figure it's from 2 to 0 because of the 0,0 and the x=2. and the anti derivative of 1/1+x^2 is tan. but I get lost when you have to take tan(2) to find area.