how to justify $\operatorname{E} [X^2] = \sigma^2 + \mu^2$ I am learning this video, which gives a justification of the formula about Sample variance.
at this time point, the teach is giving this formula
$\operatorname{E} [X^2] = \sigma^2 + \mu^2$
where does this formula come from?

this post has justified 
$$\operatorname{Var} (X) = \operatorname{E} [X^{2}] - [\operatorname{E} (X)]^{2}$$
which is the same one on your video, call it equation_1
the term on the left of that equation above $\operatorname{Var} (X) = \sigma^2$
the second term on the right of equation above $[\operatorname{E} (X)]^{2} = \mu^2$
the one as follow is the exactly same as equation_1.
$$\sigma^2 = \operatorname{E} [X^{2}] - \mu^2$$
Add $\mu^2$ to both sides
$$\sigma^2 + \mu^2 = \operatorname{E} [X^2]$$
