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This paper is devoted to explore modified $f(\mathcal{R})$ theories ofgravity using Noether symmetry approach. For this purpose,Friedmann-Robertson-Walker spacetime is chosen to investigate the cosmicevolution. The study is mainly divided into two parts: Firstly Noethersymmetries of metric $f(\mathcal{R})$ gravity are revisited and some new classof solutions with the help of conserved quantities are reported. It is shownthat different scenarios of cosmic evolution can be discussed using Noethersymmetries and one of the case indicates the chances for the existence of BigRip singularity. Secondly, $f(\mathcal{R})$ theory coupled with scalar fieldhas been discussed in detail. The Noether equations of modified gravity arereported with three subcases for flat Friedmann-Robertson-Walker universe. Itis concluded that conserved quantities are quite helpful to find some importantexact solutions in the cosmological contexts. Moreover, the scalar fieldinvolved in the modified gravity plays a vital role in the cosmic evolution andan accelerated expansion phase can be observed for some suitable choices of$f(\mathcal{R},\varphi,\chi)$ gravity models.

$f(\mathcal{R},\varphi,\chi)$ Cosmology with Noether Symmetry