The accuracy delivered by these methods is seen in the following error bounds. (Recall that the error bound is a bound on the absolute value of the difference between the actual area under the curve and its estimated value.)
For n intervals we express the error between the actual and
approximate area by 
. From page 306 of the text we have:
Trapezoidal error: 
, where M is the maximum of |f''(x)| on [a,b]
Simpson's error: 
, where K is the maximum of |f''''(x)| on [a,b]