  We prove that if the normal distribution of a singular riemannian foliation
is integrable, then each leaf of this normal distribution can be extended to be
a complete immersed totally geodesic submanifold (called section) which meets
every leaf orthogonally. In addition the set of regular points is open and
dense in each section. This result generalizes a result of Boualem and solves a
problem inspired by a remark of Palais and Terng and a work of Szenthe about
polar actions.
  We also study the singular holonomy of a singular riemannian foliation with
sections (s.r.f.s for short) and in particular the transverse orbit of the
closure of each leaf. Furthermore we prove that the closure of the leaves of a
s.r.f.s. on M form a partition of M which is a singular riemannian foliation.
This result proves partially a conjecture of Molino.
