like Gauss-Chebyshev integration formula using Lagrange polynomials

Question

Suppose that $L_k(x)$ is Lagrange Interpolation Polynomial for points $x=1,0,-1$. How to show that: $$\int_{-1}^{1}\frac{f(x)}{\sqrt{1-x^2}}dx=\sum_{k=-1}^1C_kf(k)+E$$ where $C_k=\int_{-1}^{1}\frac{L_k(x)}{\sqrt{1-x^2}}dx$.