The Length Of $r = 1 + \sin \theta$ With $x \in \left[ \frac { \pi } { 2 } , \frac { 3 \pi } { 2 } \right]$

Multiple Choice

The length of $r = 1 + \sin \theta$ with $x \in \left[ \frac { \pi } { 2 } , \frac { 3 \pi } { 2 } \right]$ is

A) 4
B) 6
C) 9
D) 12
E) 15