What rule has been applied here:
$\int_a^{b}w^2\phi(w)dw=\int_a^{b}w\phi(w)d\frac{w^2}{2}$
where $\phi(w)$ is a PDF of standard normal distribution. I am confused with $d\frac{w^2}{2}$ and how to solve this further.
Please note that this is a excerpt from calculating variance of truncated normal distribution which can be found at http://dongguo.me/me/blog/2013/12/02/gaussian-and-truncated-gaussian/ .