  Let $A$ be a DG algebra with a trivial differential over a commutative unital
ring. This paper investigates the image of the totaling functor, defined from
the category of complexes of graded $A$-modules to the category of DG
$A$-modules. Specifically, we exhibit a special class of semifree DG
$A$-modules which can always be expressed as the totaling of some complex of
graded free $A$-modules. As a corollary, we also provide results concerning the
image of the totaling functor when $A$ is a polynomial ring over a field.
