In the following work will be presented the integral of Henstock-Kurzweil that was proposed by Jaroslav Kurzweil and Ralph Henstock, studying the main results obtained in the form of the convenience of the same in front of the integral of Riemann and the one of Lebesgue. We will present some of the most relevant problems of the integrals mentioned and how the Henstock-Kurzweil integral solve problems and improve most of the results obtained in the usual and abstract integration theories. The following paper presents an alternative way of approaching significant results in the area of analysis more specifically in the theory of integration.