I realize i need to use polar coordinates. First thing i do is calculate $z=1-y$ and then include that in $z=1-x^2-y^2$ that turns out be circle centered at $ (0,\frac 12) $. I know that $ \theta$ limits of integration should be from 0 to $\pi$ but what should be limits of integration for $r$. Also then the double integral should be $$ \int_0^\pi\int_?^?[(1-r^2)-(1-rsin\theta)]rdrd\theta $$ Any help is appreciated.