I have found this problem in some exam for my numerical analysis class.
Determine a Newton-Cotes quadrature formula with Chebyshev nodes of the first kind on $[-1, 1]$. Give the approximation for the error to be like
$ R(f) \le C||f^{(4)}||_{Inf}, C \gt 0 $
I don t understand how we can obtain a Newton-Cotes-like quadrature from nodes that are not equidistant on $[-1, 1]$
If you use Chebyshev nodes, it is not Newton-Cotes anymore, because Newton-Cotes formulas are based on equidistantly distributed nodes. You need to check Gauss-Chebyshev quadrature which uses chebyshev nodes on the interval (-1,1) but you need to be sure about the weight function, $\frac{1}{\sqrt{1-x^2}}$. If your weight function is 1, you might use Gauss-Legendre quadrature.