What is MATLAB's algorithm for calculating integral error?

In the documentation for the integral function, it is stated that: "integral uses the absolute error tolerance to limit an estimate of the absolute error, q – Q, where q is the computed value of the integral and Q is the (unknown) exact value." But how does MATLAB "know" what Q is? If someone can point me to documentation or white papers that would be appreciated.

Answer 1

[Roger Stafford]

Obviously Matlab’s ‘integral’ function cannot know the exact value of the given integral since it is limited to a finite number of numerical operations. However, there are techniques that can make estimates, based on reasonable assumptions about the nature of the given integrand function, of the possible range of values of the exact integral - using presumably something like Taylor’s Theorem with a remainder and assumptions about the integrand’s higher derivatives. Their statement about absolute error can then be interpreted as an assertion that their answer also lies within such a range.