title: Self-validating integration and approximation of piecewise analytic functions
abstract: Let an analytic or a piecewise analytic function on a compact interval be given. We present algorithms that produce enclosures for the integral or the function itself. Under certain conditions on the representation of the function, this is done with the minimal order of numbers of operations. The integration algorithm is implemented and numerical comparisons to non-validating integration software are presented
keyphrases: self-validating integration piecewise analytic functions compact interval enclosures minimal order integration algorithm self-validating approximation complex interval arithmetic