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...
$\displaystyle \displaystyle \int_{a}^{b} f(x)\cdot dx \approx \sum_{k=1}^{n} a_{k} \cdot f(x_{k})$ (1)
... where the $\displaystyle x_{k}$ 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
$\displaystyle \chi$ $\displaystyle \sigma$