Use Various Trigonometric Identities to Simplify the Expression Then Integrate $\int \sin ^ { 2 } \theta \cos 5 \theta d \theta$

Multiple Choice

Use various trigonometric identities to simplify the expression then integrate.
- $\int \sin ^ { 2 } \theta \cos 5 \theta d \theta$

A) $\frac { 1 } { 10 } \sin 5 \theta - \frac { 1 } { 4 } \sin 3 \theta - \frac { 1 } { 28 } \sin 7 \theta + C$
B) $\frac { 1 } { 2 } \sin 5 \theta - \frac { 1 } { 4 } \sin 3 \theta - \frac { 1 } { 7 } \sin 7 \theta + C$
C) $\frac { 1 } { 10 } \sin 3 \theta - \frac { 1 } { 4 } \sin 5 \theta - \frac { 1 } { 28 } \sin 7 \theta + C$
D) $\frac { 1 } { 10 } \sin 5 \theta - \frac { 1 } { 4 } \sin 7 \theta - \frac { 1 } { 28 } \sin 3 \theta + C$