Integral to Infinity of Sine p x over x

Theorem

 * $\displaystyle \int_0^\infty \frac {\sin p x} p \rd x = \begin{cases} \dfrac \pi 2 & : p > 0 \\

0 & : p = 0 \\ -\dfrac \pi 2 & : p < 0 \end{cases}