## Euler Integral

Euler integration was defined by Schanuel and subsequently explored by Rota, Chen, and Klain. The Euler integral of a Function (assumed to be piecewise-constant with finitely many discontinuities) is the sum of

over the finitely many discontinuities of . The -D Euler integral can be defined for classes of functions . Euler integration is additive, so the Euler integral of equals the sum of the Euler integrals of and .