  We investigate whether the new horizon first law proposed recently still work
in $f(R)$ theory. We identify the entropy and the energy of black hole as
quantities proportional to the corresponding value of integration, supported by
the fact that the new horizon first law holds true as a consequence of
equations of motion in $f(R)$ theories. The formulas for the entropy and energy
of black hole found here are in agreement with the results obtained in
literatures. For applications, some nontrivial black hole solutions in $f(R)$
theories have been considered, the entropies and the energies of black holes in
these models are firstly computed, which may be useful for future researches.
