Newton cotes formulae proofs

1. akerman

1
I am looking for two proofs they both are based on newton cotes formulae which is is in the equi spaced points xi=a+ih with h=(b−a)/n and i=0,…,n.

First proof is for ωj=ωn−j
The second one is ∑jωj=(b−a)
ω is the weight

Does anyone have a link where its explained or can someone properly show how to prove them ?