Use Integration by Parts to Establish a Reduction Formula for the Integral

Multiple Choice

Use integration by parts to establish a reduction formula for the integral.
- $$\int \sin ^ { n } x d x$$

A) $\int \sin ^ { n } x d x = \sin ^ { n - 1 } x \cos x + ( n - 1 ) \int \sin ^ { n - 2 } x d x$
B) $\int \sin ^ { n } x d x = - \frac { 1 } { n } \sin ^ { n - 1 } x \cos x + \frac { n - 1 } { n } \int \sin ^ { n - 2 } x d x$
C) $\int \sin ^ { n } x d x = - \frac { 1 } { n } \sin ^ { n - 1 } x \cos x - \frac { n - 1 } { n } \int \sin ^ { n - 1 } x d x$
D) $\int \sin ^ { n } x d x = \sin ^ { n - 1 } x \cos x - ( n - 1 ) \int \cos x \sin ^ { n - 2 } x d x$