IfFis a continuous function on the real line andf=F′is its distributional derivative, then the continuous primitive integral of distributionfis∫abf=F(b)−F(a). This integral contains the Lebesgue, Henstock-Kurzweil, and wide Denjoy integrals. Under the Alexiewicz norm, the space of integrable distributions is a Banach space. We define the convolutionf∗g(x)=∫−∞∞f(x−y)g(y)dyforfan integrable distribution andga function of bounded variation or anL1function. Usual properties of convolutions are shown to hold: commutativity, associativity, commutation with translation. Forgof bounded variation,f∗gis uniformly continuous and we have the estimate‖f∗g‖∞≤‖f‖‖g‖ℬ𝒱, where‖f‖=supI|∫If|is the Alexiewicz norm. This supremum is taken over all intervalsI⊂ℝ. Wheng∈L1, the estimate is‖f∗g‖≤‖f‖‖g‖1. There are results on differentiation and integration of convolutions. A type of Fubini theorem is proved for the continuous primitive integral.