Help with calculus (area of region)

Find the area of the region bounded by the curve r=1+sinθ
here's the picture: http://i48.tinypic.com/2reryhi.jpg
I got B 3pi/4 and I just want to make sure that's right.
A. pi/2
B. 3pi/4
C. pi/4
D. 3pi/2

Found out when the loop touches the origin:
0 = 1 + sinθ
==> sinθ = -1
==> θ = (3π/2) + 2kπ, where k is any integer

Any two consecutive values for k will work. We'll use θ = 3π/2 and θ = 7π/2.

The area in the region is given by:
A = (1/2) ∫[a,b] r² dθ
= (1/2) ∫[3π/2,7π/2] (1 + sinθ)² dθ
= (1/2) ∫[3π/2,7π/2] sin²θ + 2sinθ + 1 dθ
= (1/2) ∫[3π/2,7π/2] (1/2)(1 - cos(2θ)) + 2sinθ + 1 dθ
= (1/2) ∫[3π/2,7π/2] (3/2) - (1/2)cos(2θ) + 2sinθ dθ
= (1/2)[(3/2)θ - (1/4)sin(2θ) - 2cosθ] from θ = 3π/2 to 7π/2
= (1/2)[(3/2)(7π/2) - (1/4)(0) - 2(0) - (3/2)(3π/2) - 0 - 0]
= (1/2)(12π/4)
= 3π/2