  Working in Einstein frame we introduce, in order to avoid singularities,
holonomy corrections to the $f(R)=R+\alpha R^2$ model. We perform a detailed
analytical and numerical study when holonomy corrections are taken into account
in both Jordan and Einstein frames obtaining, in Jordan frame, a dynamics which
differs qualitatively, at early times, from the one of the original model. More
precisely, when holonomy corrections are taken into account the universe is not
singular, starting at early times in the contracting phase and bouncing to
enter in the expanding one where, as in the original model, it inflates. This
dynamics is completely different from the one obtained in the original
$R+\alpha R^2$ model, where the universe is singular at early times and never
bounces. Moreover, we show that these holonomy corrections may lead to better
predictions for the inflationary phase as compared with current observations.
