Why is the expected value of the squared value equal to the sum of the standard deviation and the mean?

Question

I am currently reading the proof here that one has to divide by $n-1$ in order to get an unbiased estimator of the population variance.

What I do not get is this:

\begin{equation}E[y_i^2] = \sigma^2 +\mu^2\end{equation}

I extracted that portion from the difference between line three and four of the proof. Why is it true?

Answer 1

The given formula is a rewriting of the following expression for the variance (see comments above): $$ \sigma^2 = E(y^2)-\mu^2. $$