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Now I_1 is:  \begin{eqnarray}  I_1 &=& \mu \int_{-\mu/(\sqrt{2}\sigma)}^{0} \frac{2}{\sqrt{\pi}} dt \exp(-t^2) + 2 \int_{\mu^2/(2\sigma^2)}^{0} \frac{\sigma dt}{\sqrt{2\pi}}\exp(-t) \\  &=& -\mu{\rm -\mu\,{\rm  erf}\left(\frac{\mu^2}{2\sigma^2}\right) + \sqrt{\frac{2}{\pi}} \sigma\left[ \exp\left(-\frac{\mu^2}{2\sigma^2} - 1\right) \right] \end{eqnarray}