I think I figured it out, that or I completely botched it.

If x=0 and y=0, and y=x-x^2 then y=x and y=x^2, as x^2=x for 0 and 1.

So my y's are y, and root y.

Probably incorrect, but that's about as good of a guess as I could come up with. Area was pi/2.