Floor of an exponential

Let $X$ be a random variable having the probability density function $$f(x)=\begin{cases}e^{-x},&x>0\\0,&x\le 0.\end{cases}$$ Define $Y=[X]$, where $[X]$ denotes the largest integer not exceeding $X$. Then, $E\left(Y^{2}\right)$ is equal to