 Newton-Cotes quadrature is based on approximating "f" by a polynomial interpolant at equally-spaced points in , and like Clenshaw-Curtis also integrates polynomials of degree up to "n" exactly when given "n" samples.However, it suffers from Runge's phenomenon as "n" increases; Newton-Cotes does not converge for some continuous integrands "f", and when it does converge it may suffer from numerical rounding errors.Thus, both Clenshaw-Curtis and Gauss-Legendre enjoy substantial benefits over Newton-Cotes for moderate to large "n".