Integration by parts for delta integrals with sigma in integrand

Theorem

The following formula holds: $$\int_a^b f(\sigma(t))g^{\Delta}(t) \Delta t = (fg)(b) - (fg)(a) - \int_a^b f^{\Delta}(t)g(t) \Delta t,$$ where $\int$ denotes the delta integral.

See also

Integration by parts for delta integrals with no sigma in integrand