Expectation of quadratic polynomial density

Let $X$ be a random variable having the probability density function $$f(x)=\begin{cases} ax^2+b, & 0\le x\le 3 \ 0, & \text{otherwise,} \end{cases}$$ where $a$ and $b$ are real constants, and $P(X\ge 2)=\frac{2}{3}$. Then $E(X)$ equals __________ (round off to $2$ decimal places)