 However, this measure of accuracy is not generally a very useful one---polynomials are very simple to integrate and this argument does not by itself guarantee better accuracy on integrating other functions.Clenshaw-Curtis quadrature is based on approximating "f" by a polynomial interpolant at Chebyshev nodes and integrates polynomials of degree up to "n" exactly when given "n" samples.Even though it does not integrate polynomials or other functions that are analytic in a large neighborhood of as well as Gauss-Legendre quadrature, Clenshaw-Curtis converges at approximately the same rate as Gauss-Legendre quadrature for most (non-analytic) integrands.