If $E[X]=\int_{0}^{\infty}(1-F_X(t)-F_X(-t))dt$ then why $E[X^2]=\int_{0}^{\infty}(1-F_{X^2}(t))dt$

Question

I know that from definition: $E[X]=\int_{0}^{\infty}(1-F_X(t)-F_X(-t))dt$

But I encountered the following claim: $E[X^2]=\int_{0}^{\infty}(1-F_{X^2}(t))dt$

Why isn't it the same as above? hence:

$E[X^2]=\int_{0}^{\infty}(1-F_{X^2}(t)-F_{X^2}(-t))dt$

Answer 1

They are actually the same, but because $X^2$ is always non negative $F_{X^2}(-t)=0$ and the expression simplifies to the one given.