Lobatto quadrature

An $s$-node Lobatto quadrature rule includes both endpoints and is exact for polynomials of degree at most $2s-3$. On $[-1,1]$, its interior nodes are the zeros of the derivative of the degree-$(s-1)$ Legendre polynomial. The three-node rule on $[0,1]$ has nodes $0,1/2,1$ and weights $1/6,2/3,1/6$. Integrating the interpolation basis from zero to each node gives the three-stage Lobatto IIIA method.