I have an intergral and im not sure how to find the limits of integration from cartesian to polar form 0<a<1

Integral from 1 to a ( integral from square root of (1-x^2) to 0) of F(x,y) dydx

Apparently the polar form integrals are suppose to be:

Integral from 1 to a (integral from cos-1(a/r) to 0) and im not sure where that came from...

Also if i have an integral from 1 to a(integral from root(1-x^2) to 0) of (x^2 -y^2)dydx i change it to polar form

integral 1 to a( integral from cos-1(a/r) of r(r^2cos^2theta - r^2sin^2thetha)dtheta dr

I attempted this integral by integrating with respect to r first then in respect to theta but am not sure if its right..any tips?