f is obtainable from F by taking derivatives
F is obtainable from f by integration
f is
when (s,t) is in the III or IV cuadrant we have,
integrating over y,
F(s,t) = int(int(f(x,y),y=-sqrt(1-x^2)..t),x=-1..s);
FY(t) = 2*int(int(1/Pi,x=0..sqrt(1-y^2)),y=-1..t);
given by