  We give an alternative definition of integral at the generality of the Perron
integral and propose an exposition of the foundations of integral theory
starting from this new definition. Both definition and proofs needed for the
development are unexpectedly simple. We show how to adapt the definition to
cover the multidimensional and Stieltjes case and prove that our integral is
equivalent to the Henstock-Kurzweil(-Stieltjes) integral.
