Any code should be written in MATLAB; And help would be great

Problem 1. Prove that the closed Newton-Cotes rule QNC(m) will compute the integral exactly for k = 1, 2, , m. Here the quadrature nodes are the fixed points zj = (j-1)/(m-1) for j- 1,2, .,m. Therefore, the weights wi,2.,wm satisfy k-1 These conditions define a linear system. Write a function ComputeClosedNewtonCotesWeights to solve this system for the weights (returning vector of coefficients), and compare your computed weights with those given by M. Abramowitz and I. Stegun (in ClosedNewtonCotesweights these weights are hardcoded). For comparison you can use a norm of the following defference vector norm (ComputeNewtonCotesClosedWeights (m)-NewtonCotesClosedWeights (m)) Problem 1. Prove that the closed Newton-Cotes rule QNC(m) will compute the integral exactly for k = 1, 2, , m. Here the quadrature nodes are the fixed points zj = (j-1)/(m-1) for j- 1,2, .,m. Therefore, the weights wi,2.,wm satisfy k-1 These conditions define a linear system. Write a function ComputeClosedNewtonCotesWeights to solve this system for the weights (returning vector of coefficients), and compare your computed weights with those given by M. Abramowitz and I. Stegun (in ClosedNewtonCotesweights these weights are hardcoded). For comparison you can use a norm of the following defference vector norm (ComputeNewtonCotesClosedWeights (m)-NewtonCotesClosedWeights (m))