Lineability of Denjoy Integrable Function

Gordon presented an example of a function that is Denjoy integrable but not Lebesgue integrable in the book: The integrals of Lebesgue, Denjoy, Peron and Henstock. That example showed that, the class of Denjoy integrable functions is larger than the class of Lebesgue integrable functions. We are going to show that the set of Denjoy inte-grable functions that are not Lebesgue integrable, contains an infinite dimensional vector space.