  Let $\tilde{N}\_{t}$ be a standard compensated Poisson process on $[0,1]$. We
prove a new characterization of anticipating integrals of the Skorohod type
with respect to $\tilde{N}$, and use it to obtain several counterparts to well
established properties of semimartingale stochastic integrals. In particular we
show that, if the integrand is sufficiently regular, anticipating Skorohod
integral processes with respect to $\tilde{N}$ admit a pointwise representation
as usual It\^{o} integrals in an independently enlarged filtration. We apply
such a result to: (i) characterize Skorohod integral processes in terms of
products of backward and forward Poisson martingales, (ii) develop a new
It\^{o}-type calculus for anticipating integrals on the Poisson space, and
(iii) write Burkholder-type inequalities for Skorohod integrals.
