Find the area of the region

Find the area of the region bounded by the (the rest of the problem is in the picture below: http://i46.tinypic.com/25hg32u.jpg
how do I do this...can someone show the work and explain.
A. 3/2
B. 3pi/4
C. 3pi
D. 3/2pi

Area = (1/2) ∫ r^2 dθ

= (1/2) ∫ (1 +cos θ)^2 dθ --- integrate from 0 to 2π
= (1/2) ∫ (1+ 2 cos θ + cos^2 θ) dθ

= (1/2) ∫ dθ + ∫ cos θ dθ + (1/2) ∫ cos^2 θ dθ

= θ/2 + sin θ + (1/2) ∫ (1+ cos 2θ) /2 dθ
= θ/2 + sin θ + θ/4 + (1/4) ∫ cos 2θ dθ ----------(1)

∫ cos 2θ dθ
Let u = 2θ
du = 2 dθ
dθ = (1/2) du
∫ cos 2θ dθ = (1/2) ∫ cos u du = sin u /2 = sin 2θ /2 ---(2)

substitute (2) into (1)
= θ/2 + sin θ + θ/4 + (1/8) sin 2θ
Substitute the upper limit 2π
= 3π/2
Substitute the lower limit 0, it is 0.

Area = (1/2) ∫ r^2 dθ = 3π/2