Im bit stuck in deriving TailVar, especially from the 2nd line to 3rd line where the bounds of the integral change due to a shifting to a standard normal distribution. Please help.
They've made a substitution... But to be honest, that's not the easiest way to proceed. Starting from the second line, it's easier to use the formula for the truncated moments of a normal distribution on page 18 of the Tables with L equal to minus infinity and U equal to minus VaR. Try that instead.