Some simple numerical integration functions (using the trapezoidal rule and Simpson’s Rule) were included in the Eval2 spreadsheet, presented on Daily Download Day 15, but for purposes were better accuracy and/or higher speed are required more sophisticated methods will do a much better job.

The spreadsheet Eval-Integration.xlsb combines the Eval function with a variety of high performance integration functions, including functions from the ALGLIB library, and the Tanh_Sinh function written by Graeme Dennes (of which more below).
Download file: http://www.interactiveds.com.au/software/Eval-Integration.xlsb

The development of the integration routines started with Gaussian Quadrature, followed by Eval.xls and the ALGLIB integration functions.  Graeme Dennes’ Tanh-Sinh functions made their first appearance in Faster Integration with the Tanh-Sinh Method, and these have had several updates with a variety of functions for special cases, and extensive documentation.  Post on this method include:
Tanh-Sinh Quadrature update
Tanh-Sinh Quadrature Update 2
Tanh-Sinh Quadrature V2.0
Tanh-Sinh Quadrature V2.1
Tanh-Sinh Quadrature V3.0
and the latest version: Tanh-Sinh Quadrature V4.0

Download file: http://interactiveds.com.au/software/Tanh-Sinh and DE Quadrature by Graeme Dennes.zip

Tanh_Sinh Integration Function, with associated graph