Numerical Analysis, Numerical Integration.
representation of what is happening. Below in purple is the degree 3 polynomial f(x)=x³+x²+x+1 and in red is its remainder polynomial R(x)=(4x/3)+(4/3) which is of degree 1. Over the bounds [-1,1], these two polynomials have the exact same area, (8/3) or 2.66 repeating. This fact can be seen based