Suppose that C_kf(x_k) is the Gaussian quadrature formula, show that:
a) ∑ c_k = b - a.
b) ∫ f L_n-1,i(x)dx = ∫ f L_2-1,i(x)dx, where L_n-1,i(x) (i = 1,...,n) is the Lagrange coefficient polynomial with degree n - 1 using the nodes x_1, and so on.