Simpson's rule won't work unless . Is your n correct?
I found that from midpoint rule gives 0.88420, trapezoidal rule gives 0.87704, and simpson's rule gives 0.82994. The next question asks me to
Compute the error esimates for midpoint, trapezoidal, simpson's. Carefully examine the extreme values of f ''(x). You may use that |f ''''(x)| < 12 for 0<x<2. (the < signs all mean less than or equal to).
How would you do this?