expected value of sum of continuous random variables, abst value pdf

Question

pdf for random variable X is given by $f(x)= |x-1|$ if $0\leq x\leq 2,$ or $f(x)=0$ otherwise.

Find $E[X^{2}+X].$ The book gives the answer as $\frac{13}{6}$

I have found that $E[X^{2}]=1$ and $E[X]=\frac{3}{2}$, so why isn't the answer $\frac{5}{2}?$

Answer 1

The answer is $5/2$ (though I think you switched $E(X)$ and $E(X^2)$). I think, assuming your transcription is right, that the book is simply wrong.

Answer 2

$E(X)=1$ and $E(X^{2})=\frac{3}{2}$ so $E(X^{2}+X)=E(X^{2})+E(X)=\frac{5}{2}.$