simpson 1/3 rule (prove approx. which comes out in the course of deriving Simpsons's 3/8 rule)

[Leons]

can someone help me, i already try but im stuck

Notice that Simpson's 3/8 rule can be derived by integrating the third-degree Lagrange interpolating polynomial that fits to four equally spaced points, $$x_0, x_1, x_2, x_3$$ Prove

$$\int_{x_0}^{x_3} \frac{(x-x_1)(x-x_2)(x-x_3)}{(x_0-x_1)(x_0-x_2)(x_0-x_3)} f(x_0)\,dx \approx \frac {3h}{8} f(x_0) ,$$
which comes out in the course of deriving Simpsons's 3/8 rule

 

[blamocur]

I believe the introduction of 'a' and 'b' made the whole thing unmanageable. Could it be easier to expand the numerator to cubic polynomial and integrate that?