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How to directly compute an integral which corresponds to the normal distribution

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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    See this [Wikipedia](http://en.wikipedia.org/wiki/Normal_distribution#Numerical_approximations_for_the_normal_$C$DF) page for suggestions.2019-04-09

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You should look into the error function and its approximations

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