  The process of integration was a subject of significant development during
the last century. Despite that the Lebesgue integral is complete and has many
good properties, its inability to integrate all derivatives prompted the
introduction of new approaches - Denjoy, Perron and others introduced new ways
of integration aimed at preserving the good properties of the Lebesgue integral
but extending the set of functions to which it could be applied. The goal was
achieved but neither of the new approaches was elegant or simple or
transparent. In the 50s a new integral was introduced, independently by
Kurzweil and Henstock,in a very simple, Riemann like way, but it turned out
that it was more powerful than the Lebesgue integral. There are many names
attached to this integral, I will use here the name Henstock integral. The goal
of this article is to introduce the generalized Riemann integral and the
Lebesgue integral using generalized sequences.
