I think you mean Newton-Cotes quadrature, but be careful. “Newton’s method” will 100% of the time be taken to mean the Newton-Raphson root finding method instea

I think you mean Newton-Cotes quadrature, but be careful. “Newton’s method” will 100% of the time be taken to mean the Newton-Raphson root finding method instead, which is widely taught as “Newton’s method” (while in quadrature it’s always referred to as Newton-Cotes).