  We consider the cosmology derived from $f(T,B)$ gravity where $T$ is the
torsion scalar and $B=\frac{2}{e}\partial_{\mu}(e T^{\mu})$ a boundary term. In
particular we discuss how it is possible to recover, under the same standard,
the teleparallel $f(T)$ gravity, the curvature $f(R)$ gravity and the
teleparallel-curvature $f(R,T)$ gravity, which are particular cases of
$f(T,B)$. We adopt the Noether Symmetry Approach to study the related dynamical
systems and to find out cosmological solutions.
