  We consider super Yang-Mills theory on supermanifolds $\mathcal{M}^{(D|m)}$
using integral forms. The latter are used to define a geometric theory of
integration and are essential for a consistent action principle. The
construction relies on Picture Changing Operators $\mathbb{Y}^{(0|m)}$,
analogous to those introduced in String Theory, that admit the geometric
interpretation of Poincar\'e duals of closed submanifolds of superspace
$\mathcal{S}^{(D|0)} \subset \mathcal{M}^{(D|m)}$ having maximal bosonic
dimension $D$. We discuss the case of Super-Yang-Mills theory in $D=10$ with
$\mathcal{N}=1$ supersymmetry and we show how to retrieve its pure-spinor
formulation from the rheonomic lagrangian $\mathcal{L}_{rheo}$ of D'Auria,
Fr\'e and Da Silva, choosing a suitable $\mathbb{Y}^{(0|m)}_{ps}$. From the
same lagrangian $\mathcal{L}_{rheo}$, with another choice
$\mathbb{Y}^{(0|m)}_{comp}$ of the PCO, one retrieves the component form of the
SYM action. Equivalence of the formulations is ensured when the corresponding
PCO.s are cohomologous, which is true, in this case, of
$\mathbb{Y}^{(0|m)}_{ps}$ and $\mathbb{Y}^{(0|m)}_{comp}$.
