Newton-Cotes quadrature rules become unstable for high orders. In this paper, the author reviews two techniques to construct stable high-order quadrature rules using

$N$ equidistant quadrature points. The first method is based on results of

*M. W. Wilson* [Math. Comput. 24, 271–282 (1970;

Zbl 0219.65028)]. The second approach uses nonnegative least squares methods of

*C. L. Lawson* and

*R. J. Hanson* [Solving least squares problems, SIAM Philadelphia (1995;

Zbl 0860.65029)]. The stability follows from the fact that all weights are positive. These results can be achieved in the case

$N\sim {d}^{2}$, where

$d$ is the polynomial order of accuracy. Then the computed approximation corresponds implicitly to the integral of a (discrete) least squares approximation of the (sampled) integrand. The author shows how the underlying discrete least squares approximation can be optimized for the numerical integration. Numerical tests are presented.