Im having trouble with my limits, and whether or not im on the right direction

My question is:

Let R be the region in the first quadrant bounded by the line y=x and the curve

x^4 + (xy)^2 = y^2.

My double integral is

(1+ x^2 + y^2)^-2 dA

heres what im doing so far..

and then evaluate..Am i right, limits correct and everything

IN THE FUNCTION, SHOULD BE R/(1 + R^2)^2