Undergrad How does one derived the error bound for approximations?

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The discussion focuses on deriving error bounds for numerical approximation methods, specifically the trapezoidal rule, midpoint rule, and Simpson's rule. Participants seek clarification on the formulas used to establish these error bounds. The provided link directs users to a resource that details the derivation process in Chapter 5. Understanding these error bounds is crucial for assessing the accuracy of numerical approximations in calculus. The conversation emphasizes the importance of mastering these derivations for effective application in mathematical problems.
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error bounds for trapezoidal rule, midpoint rule, and Simpson's rule. can anyone please show me how to derive the formula?
 
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