For a positive integer n, an n-point Gauss–Legendre rule uses the n roots of the degree-n Legendre polynomial and their corresponding weights. For unweighted integration on [-1,1], the ideal mathematical rule integrates every polynomial of degree at most 2n−1 exactly. This guarantee does not extend to arbitrary functions or all higher-degree polynomials. Numerical approximations to nodes, weights, and arithmetic can introduce error; this caveat is a scoped inference, not a universal library error bound.

Source: https://dlmf.nist.gov/3.5