Let x1, . . . , xn [a, b], w1, . . . , wn R be the nodes and the weight of a quadrature formula. Assume that wj < 0 for some j {1, . . . , n}. Construct a continuous function f : [a, b] R such that f(x) 0, x [a, b], i.e.,

Integral from a to b of f(x)dx > 0, but Sum from i=1 to n of wif(xi) < 0.