\displaystyle  = \frac{\sqrt{2}\sigma}{\sqrt{\pi}} \left( \int_{-\infty}^{0}  u  e^{ - u^2 } \, du + \int_{0}^{\infty}  u  e^{ - u^2 } \, du \right ) +  \frac{\mu}{\sqrt{\pi}} \int_{-\infty}^{\infty} e^{ - u^2 } \, du