lecture 9 typo:  (page 7)

The linear polynomial formed using the points 0 and h should actually be:

P_1(x) = f(0)*(x-h)/(-h) + f(h)*x/h

(missing sign in f(0) denominator.)

Then the integral evaluates to the correct answer.  As it currently stands, the integral is incorrectly evaluated to the correct answer.