Reduction Formula for Integral of Power of Sine

Theorem
Let $n \in \Z_{> 0}$ be a (strictly) positive integer.

Let:
 * $I_n := \ds \int \sin^n x \rd x$

Then:
 * $I_n = \dfrac {n - 1} n I_{n - 2} - \dfrac {\sin^{n - 1} x \cos x} n$

is a reduction formula for $\ds \int \sin^n x \rd x$.

Also see

 * Reduction Formula for Integral of Power of Cosine
 * Reduction Formula for Integral of Power of Tangent