From Cartesian coordinates to polar coordinates Integral

how do i turn the double integral : int{x=0 --> x=1} int{y=-sqrt(1-x^2) -->sqrt(1-x^2)} x+y dydx into polar coordinates integral

thank you!

Note that the bounds of integration represent the right half of the unit disk x^2 + y^2 ≤ 1.

So converting to polar coordinates yields
∫(θ = -π/2 to π/2) ∫(r = 0 to 1) (r cos θ + r sin θ) * r dr dθ
= ∫(θ = -π/2 to π/2) (cos θ + sin θ) dθ * ∫(r = 0 to 1) r^2 dr
= ∫(θ = -π/2 to π/2) (cos θ + 0) dθ * ∫(r = 0 to 1) r^2 dr, via odd integrand
= 2 ∫(θ = 0 to π/2) cos θ dθ * ∫(r = 0 to 1) r^2 dr, via even integrand
= 2 * 1 * 1/3
= 2/3.

I hope this helps!