`y = x/(x^2 + 1)^2,` `y = x^5 - x,` `xgt=0` Use a graph to find approximate x-coordinates of the points of intersection of the given curves. Then...

We can see that these graphs intersect at x = 0, and around x = 1. A little greater than x = 1.

In order to approximate the area of this region we take the integral of the top function minus the bottom function from x = 0 to x = 1.

`int_0^1 x/(x^2 + 1)^2 - (x^5 - x) dx`

We can use u sub to find the integral of the first part, which will equal 

`-1/(2(x^2 + 1))`

And the second part is just a simple power rule. So we get:

`-1/(2(x^2 + 1)) - x^6/6 - x^2/2 `  from 0 to 1.

When evaluated gets us 7/12, or about .5833