Abstract—We investigate the common features and the resemblance of the central parts of the different existing integration theories to obtain a more unified approach to the notion of integral. Our approach gives a presentation of the integral that does not require the development of measure theory.

Index Terms—Riemann, Lebesgue-Bochner, Henstock-Kurzweil, McShane, Bartle integrals.

The author is with Private Bag 0022, Department of Mathematics, University of Botswana, Gaborone (email: robdera@yahoo.com).

Cite: Mangatiana A. Robdera, "A Unified Approach to Integration Theory," International Journal of Applied Physics and Mathematics vol. 9, no. 1, pp. 21-28, 2019.