  In the context of the integration over algebras introduced in a previous
paper, we obtain several results for a particular class of associative algebras
with identity. The algebras of this class are called self-conjugated, and they
include, for instance, the paragrassmann algebras of order $p$, the
quaternionic algebra and the toroidal algebras. We study the relation between
derivations and integration, proving a generalization of the standard result
for the Riemann integral about the translational invariance of the measure and
the vanishing of the integral of a total derivative (for convenient boundary
conditions). We consider also the possibility, given the integration over an
algebra, to define from it the integral over a subalgebra, in a way similar to
the usual integration over manifolds. That is projecting out the submanifold in
the integration measure. We prove that this is possible for paragrassmann
algebras of order $p$, once we consider them as subalgebras of the algebra of
the $(p+1)\times(p+1)$ matrices. We find also that the integration over the
subalgebra coincides with the integral defined in the direct way. As a
by-product we can define the integration over a one-dimensional Grassmann
algebra as a trace over $2\times 2$ matrices.
