How can N data points match a polynomial of order 2N-1? There is not a match of f(x) at every x, instead there is a match to the overall integral. If N=2 points, then 2N-1 = 3 and a cubic f(x) is integrated exactly. But with N=2 points, then a linear approximation is integrated, There is (-) error for some (x) values and (+) error for others. But the overall integral from (a) to (b) is matched by exactly locating the optimal GQ at precisely the correct points so that the (+) and (-) errors will cancel. The optimal Gauss Quadrature points are tabulated in standard form based on integration from (-1) to (+1) over an interval of base width of two. The left limit x=a corresponds to x=-1 and the right limit x=b corresponds to F=+1. Thus the mid-point x = (a+b)/2 is 50 and the scale factor for the integral is {(b- a)/2). The independent variable mapping from a