Deriving weights for closed newton-cotes formula

Question

Assignment:

(By hand only, no programming, but you are encouraged to use Mathematica to assist with the algebra)

Derive all of the weights for the closed Newton-Cotes formula for n=4(the so-called Milne rule). Find the w₂ weight for the n=6 case. How do you know if you are correct in this case?

Provide complete and step by step solution for the question and show calculations and use formulas.