  We show that several integrable (i.e., exactly solvable) scalar cosmologies
considered by Fr\'e, Sagnotti and Sorin (Nuclear Physics \textbf{B 877}(3)
(2013), 1028--1106) can be generalized to include cases where the spatial
curvature is not zero and, besides a scalar field, matter or radiation are
present with an equation of state $p^{(m)} = w\, \rho^{(m)}$; depending on the
specific form of the self-interaction potential for the field, the constant $w$
can be arbitrary or must be fixed suitably.
