  In this article in a generalization of our previous work, we investigate the
dynamics of the non-local $F(R)$ gravity after casting it into local form. The
non-singular bouncing behavior and quintom model of dark energy are achieved
without involving negative kinetic energy fields. Two cosmological tests are
performed to constrain the model parameters. In case of phantom crossing the
distance modulus predicted by the model best-fits the observational data. In
comparison with the CPL parametrization for drift velocity, the model in some
redshift intervals is in good agreement with the data.
