The author defines a new integral, the regulated primitive integral. A function on the real line is called regulated if it has a left limit and a right limit at each point. If \(f\) is a Schwartz distribution on the real line such that \(f=F'\) (distributional or weak derivative) for a regulated function F then the regulated primitive integral of \(f\) on an interval \([a,b]\) is \(\int _a ^b f= F(b-) - F (a+)\). Then the author shows that the space of integrable distributions is a Banach space and Banach lattice under the Alexiewicz norm, and this space contains the spaces of Lebesgue and Henstock-Kurzweil integrable functions. The author also proves that the space is the completion of the space of signed Radon measures in the Alexiewicz norm and the functions of bounded variation form the dual space and the space of multipliers. Moreover, the author proves some properties of this integral such as integration by parts, change of variables, Hölder’s inequality, Taylor’s theorem and a convergence theorem.