Integrate the five Lagrange interpolation polynomials at the equally spaced nodes to obtain the displayed rule. It is exact for polynomials through degree four, and symmetry also makes it exact in degree five. Symmetric endpoint, inner-node and midpoint weights satisfy , , , giving , , .
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Boole's rule, also known as Boole's theorem or Boole's quadrature formula, is a numerical integration method that can be used to approximate the definite integral of a function. It is particularly useful for numerical integration of tabulated data points and is based on the idea of fitting a polynomial to the data and then integrating that polynomial. The rule is named after the mathematician George Boole, known for his contributions to algebra and logic.