This work takes as a starting point the numerical quadrature formula based on Lagrange interpolating polynomials. From this formula we obtain the numerical quadrature rules at five and six simple nodes with their respective errors. Then the concept of composite integration is used to subdivide the integration interval and apply the simple numerical quadrature to each and every subdivision of the integration interval. From which the five-node and six-node composite numerical quadrature rules with their respective errors are derived. All the deduced rules are illustrated by means of examples.