Can anyone please help me with this integral? There are tricks you can pull off to do the integral when the upper limit is infinity, but it gets difficult when the upper limit is a per-specified number. Here f(x)=x or constant. Basically, I want to compute the expected value of f(x) using a normal (non-standard) distribution. I would like to be able to express the result in terms of C (upper limit), the mean and the standard deviation of the normal distribution. Thank you!
$$ \int_{ - \infty }^c {f(x){1 \over {\sqrt {2\pi } \sigma }} e^{ - {1 \over 2}\left( {{{x - \mu } \over \sigma }} \right)^{\,2} } dx} $$
Actually, this is very a simple question. I may have been just stupid. It only gets tricky when f(x) is a constant where you would need to use erf function. It is trivia when f(x) = x...