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I_1(\mu, \sigma) = \frac{\mu}{2} + \int_{0}^{\infty} \frac{\sigma dt}{\sqrt{2\pi}}\exp(-t) = \frac{\mu}{2} + \frac{\sigma}{\sqrt{2\pi}}   \end{equation}  Now let us consider I_2.  \begin{equation}  \,\, I_2(\mu, \sigma)  = 2 \int_{-\mu}^{\infty} \int_{-\mu}^{0}  \frac{(y+\mu)}{\sqrt{2\pi}\sigma}\exp\left(-\frac{y^2}{2\sigma^2}\right)dy \\ \end{equation}  \begin{equation}   \,\, = 2 \int_{-\mu}^{0} dy\frac{(y+\mu)}{\sqrt{2\pi}\sigma}\exp\left(-\frac{y^2}{2\sigma^2}\right) + 2 \int_{0}^{\infty} dy\frac{(y+\mu)}{\sqrt{2\pi}\sigma}\exp\left(-\frac{y^2}{2\sigma^2}\right) \\