Pdf of a function of a random variable

I am supposed to fin the pdf f $\displaystyle Y = e^X$ where $\displaystyle X$ is normal r.v. with parameters $\displaystyle \mu, \sigma^2$

The pdf of X is

$\displaystyle \frac{1}{ \sqrt{2\pi\sigma^2}}e^{-\frac{(x-\mu)^2}{2\sigma^2}}$

(Sorry I can't get this to appear in tex for some reason)

If I integrate this function from negative infinity to ln(y), then differeniate with respect to y, I should get the function I seek.

However I am not sure how to integrate the normal distribution function, could someone please explain to me some way I way go about doing that?

Thank you for your help.