3rd International E-Conference on Mathematical Advances and Applications, İstanbul, Turkey, 24 - 27 June 2020, pp.119
Henstock-Kurzweil integral, known as gauge integral or generalized Riemann integral, is defined based on the modified Riemann sum. It extends the Lebesgue integral so that it has a wider class of integrable functions. That is, the Lebesgue integrability implies Henstock-Kurzweil integrability, however the converse is not necessarily true. Furthermore, it has some applications in mathematics, computer science and engineering. In this work, we examine the Henstock-Kurzweil integral and present its fundamental properites and some examples, especially functions that are Henstock-Kurzweil integrable but not Lebesgue integrable. Finally, we study the relationship between Henstock-Kurzweil integral and Lebesgue integral.