Well the title says it all:
Can someone please help me integrate:
$$\int_0^{500} e^{\frac{-(x-a)^2}{b^2}} \, dx$$
I need to understand how $e$ can be integrated when it is to the power of a polynomial. Another example that would help with my understanding is how someone would integrate:
$$\int_0^{500} e^{\frac{-x^2 + 4ax - 2a^2}{b^2}} \, dx$$
$a$ and $b$ are constants in this case.
Any help would be appreciated.