I have no idea how to start to solve it.
Thank you...
Probably it is a particular application of gaussian quadrature...
Gaussian Quadrature -- from Wolfram MathWorld
The gaussian quadrature approximate a definite integral as...
(1)
... where the are the zeroes of the Legendre polynomial of degree n. An interesting property of the gaussian quadrature is that the error vanishes if f(*) is a polynomial of degree less or equal to 2n-1, and that situation is achieved if n=3 and f(*) is a polynomial of degree 5 or less...
Kind regards