  We establish an integration theory for singular subalgebroids, by
diffeological groupoids. To do so, we single out a class of diffeological
groupoids satisfying specific properties, and we introduce a
differentiation-integration procedure under which they correspond to singular
subalgebroids. Our definition of integration distinguishes the holonomy
groupoid from the graph, although both differentiate to the original singular
subalgebroid: the holonomy groupoid satisfies a certain submersive property,
while the graph does not.
