$\displaystyle y=x^2

y=\frac{2}{x^2+1}

$

intersects at + or - 1

so integral would be$\displaystyle

2\int_{-1}^1 \frac{2}{x^2+1}-x^2dx$

after reducing, I got $\displaystyle 2\int_{-1}^1 \frac{1-x^2}{x^2+1}dx$

Don't know how to find anti derivative from here...

I just looked in the back for the answer and it is pi-2/3

is there some sort of trig identity going on....