In this paper we study the Denjoy-Riemann and Denjoy-McShane integrals of functions mapping an interval $\left[a,b\right]$ into a Banach space $X.$ It is shown that a Denjoy-Bochner integrable function on $\left[a,b\right]$ is Denjoy-Riemann integrable on $\left[a,b\right]$, that a Denjoy-Riemann integrable function on $\left[a,b\right]$ is Denjoy-McShane integrable on $\left[a,b\right]$ and that a Denjoy-McShane integrable function on $\left[a,b\right]$ is Denjoy-Pettis integrable on $\left[a,b\right].$ In addition, it is shown that for spaces that do not contain a copy of $c_0$, a measurable Denjoy-McShane integrable...