Second moment of a piecewise density

Let $X$ be a continuous random variable with the probability density function

$$f(x)=\begin{cases}ax^2, & 0<x<1,\ bx^{-4}, & x\ge1,\ 0, & \text{otherwise,}\end{cases}$$

where $a$ and $b$ are positive real numbers. If $E(X)=1$, then $E(X^2)$ equals __________