  Using the singularity analysis, we investigate the integrability properties
and existence of analytic solutions in $f\left( R\right)$-cosmology.
Specifically, for some power-law $f\left( R\right) $-theories of particular
interest, we apply the ARS algorithm to prove if the field equations possess
the Painlev\'{e} property. Constraints for the free parameters of the power-law
models are derived, and new analytic solutions are derived, expressed in terms
of Laurent expansions.
