Find the exact coordinates of the centroid of the lamina bounded by the curve y=1/(1+x^2), the x-axis, the y-axis, and x=1.

I got the Area to be (Pi/4)

For X-Bar, I got: (2/Pi)*ln(2)

I got stuck on the Y-Bar.

I got;

(4/Pi)*(1/2)*the integaral (1/(1+x^2)^2) dx.

This comes to (2/Pi)*the integral (1/(1+x^2)^2) dx.

I don't know how to integrate that. So can someone tell me if my area and X-Bar are correct and then help me integrate for Y-Bar?