I am given a pdf $f(x) = |x-1|$ for $0 \leq x \leq 2,$ 0 otherwise, and asked to find expected value of $X^{2} + X.$ I simply integrated $(x^{2} + x)|x-1|$ from 0 to 2, checked with mathematica, and got $\frac{5}{2}.$ The answer in the back of the book, however, is $\frac{13}6.$ What am I doing wrong?
Thanks.