# Definite integral of Normal Distribution [duplicate]

Is there any approximate solution for the following definite integral of normal distribution?

$$\int_{a}^{b} e^{-\frac{(x-\mu)^2}{2s^2}} \ dx$$

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## marked as duplicate by Qiaochu YuanMay 30 '11 at 9:00

$$\frac{1}{\sqrt{2\pi}\sigma}\int_a^b e^{\frac{-(x-\mu)^2}{2\sigma^2}}\ dx=\frac{1}{2}\left[\text{erf}\left(\frac{b-\mu}{\sqrt{2}\sigma}\right)-\text{erf}\left(\frac{a-\mu}{\sqrt{2}\sigma}\right)\right]$$