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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/ .

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    It's a way of proceeding with integration by parts – 2017-02-09
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    @Test123 I would be very thankful if you could provide a link with similar (perhaps simpler) solved example. – 2017-02-09
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    Check this: http://mathworld.wolfram.com/IntegrationbyParts.html – 2017-02-09
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    @Test123 I still cannot see how to integrate this to get the final result. – 2017-02-23

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