If $\displaystyle X \sim N( \mu , {\sigma}^2)$, then how do you derive the density of $\displaystyle Y = |X| $?

This is what I did:

$\displaystyle F_{y}(y) = P(Y < y) $

$\displaystyle F_{y}(y) = P(|X| < y) $

$\displaystyle F_{y}(y) = \left\{\begin{array}{cc}P(X< y),&\mbox{ if }

x > 0 \\ P(-X <y), & \mbox{ if } x<0\end{array}\right. $

Is this right so far?