  The integrability of higher-order theories of gravity is of importance in the
determining the properties of these models and so their viability as models of
reality. An important tool in the establishment of integrability is the
singularity analysis. We apply this analysis to the case of fourth-order theory
of gravity $f(R) = R + qR^{n}$ to establish those values of the free parameters
$q$ and $n$ for which integrability in this sense exists. As a prelininary we
examine the well-known case of $n = 4/3$.
