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I found that from midpoint rule gives 0.88420, trapezoidal rule gives 0.87704, and simpson's rule gives 0.82994.

Then it 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).

I found that EM=0.14875, ET=0.07438, ES=0.13333

do my answers seem correct?

My question is how big should we take n to guarntee absolute value of ET <0.0001? and for EM<0.0001 and ES<0.0001?

How would you figure this question out?