Let X and Y have jointed pdf: fxy = (x+y) for 0<=x<=1 , 0<=y<= 1

Find p[XX2 ], p[X+Y>0.5]

In this question, I understand how to calculate double integrals. My main problem is: how to define the boundaries in the each integral?

For example, in p[X

but in the second one (p[Y< X2 ]), it would be (integral)1 and x=0 and (integral)X^2 and y=0

Thank you