For the cdf, calculate the $\displaystyle E[X^3 +1]$

$\displaystyle F(x)=\left\{\begin{array}{cc}0&\mbox{ if }x< 0\\

{1\over 4} x^2 & \mbox{ if } 0 \leq x \leq 2\\

1 &\mbox{ if } x >2\end{array}\right.$

I get:

$\displaystyle E[X^3 +1]=E[X^3] +E[1]= \int_{0}^{2} x^3.{1 \over 2}xdx +1

=\left[{x^5 \over 10}\right]^2_0 +1= {32 \over 10} +1 = {42 \over 10}$

is that correct?