  This paper is devoted to investigate $f(R)$ gravity using Noether symmetry
approach. For this purpose, we consider Friedmann Robertson-Walker (FRW)
universe and spherically symmetric spacetimes. The Noether symmetry generators
are evaluated for some specific choice of $f(R)$ models in the presence of
gauge term. Further, we calculate the corresponding conserved quantities in
each case. Moreover, the importance and stability criteria of these models are
discussed.
