We describe methods for the numerical calculation of integrals with verified error bounds. The problems range from integration over an interval to integration of parameter-dependent integrands over the whole d-variate space. It is argued, why we use bounds for the integrands in the complex plane as a tool for bounding the error in our own integration software. © 2006 Elsevier B.V. All rights reserved.
Petras, K. (2007). Principles of verified numerical integration. Journal of Computational and Applied Mathematics, 199(2), 317–328. https://doi.org/10.1016/j.cam.2005.07.040