  Higher-order corrections of Einstein-Hilbert action of general relativity can
be recovered by imposing the existence of a Noether symmetry to a class of
theories of gravity where Ricci scalar R and its d'Alembertian $\Box R$ are
present. In several cases, it is possible to get exact cosmological solutions
or, at least, to simplify dynamics by recovering constants of motion. The main
result is that a Noether vector seems to rule the presence of higher-order
corrections of gravitaty.
