A note on Kurzweil-Henstock's anticipating non-stochastic integral

Motivated by the study of anticipating stochastic integrals using Kurzweil-Henstock approach, we use anticipating interval-point pairs (with the tag as the right-end point of the interval) in studying non-stochastic integral, which we call the Kurzweil-Henstock anticipating non-stochastic integral. We prove the integration-by-parts and integration-by-substitution results, the convergence theorems using our new setting. Using the convergence theorems, we show that the Kurzweil-Henstock's anticipating non-stochastic integral is equivalent to the Lebesgue integral.