Area between y = x² and y = 2/(x² + 1)

[tmt1]

Hi,

I have this problem to find the area between 2 curves:

$y = x^2$

and

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

I found that the points of intersection are -1 and 1 and it is symmetrical.

I get
$2\int_{0}^{1} \ \frac{1}{x^2 + 1} - x^2 dx$which I am unable to solve. I have tried u-substitution but I end up getting mixed up.

Thanks

 

[Siron]

There's a standard integral involved:
$$\int \frac{dx}{x^2+1} = \arctan(x)$$

I think you can figure out the answer right now ;)