Find the area of the region bounded by: r=5−2sin(theta)

I am confused and lost in calc II... Please help me!

int(r^2 * dt) =>
int((25 - 20sin(t) + 4sin(t)^2) * dt) =>
int(25 * dt) - int(20 * sin(t) * dt) + int(4 * sin(t)^2 * dt) =>
25t + 20cos(t) + 4 * int(sin(2t/2)^2 * dt) =>
25t + 20cos(t) + 4 * int((1/2) * (1 - cos(2t)) * dt) =>
25 * t + 20 * cos(t) + 4 * (1/2) * (t - (1/2) * sin(2t)) + C =>
25 * t + 20 * cos(t) + 2t - sin(2t) + C =>
27 * t + 20 * cos(t) - sin(2t) + C

Plug in your bounds and you're set

27 * (2pi - 0) + 20 * (cos(2pi) - cos(0)) - (sin(4pi) - sin(0)) =>
54pi + 0 - 0 =>
54pi