  Gravitationally coupled scalar fields $\phi $, distinguished by the choice of
an effective self-interaction potential $V(\phi )$, simulating a temporarily
non-vanishing cosmological term, can generate both inflation and late time
acceleration. In scalar field cosmological models the evolution of the Hubble
function is determined, in terms of the interaction potential, by a Riccati
type equation. In the present work we investigate scalar field cosmological
models that can be obtained as solutions of the Riccati evolution equation for
the Hubble function. Four exact integrability cases of the field equations are
presented, representing classes of general solutions of the Riccati evolution
equation. The solutions correspond to cosmological models in which the Hubble
function is proportional to the scalar field potential plus a linearly
decreasing function of time, models with the time variation of the scalar field
potential proportional to the potential minus its square, models in which the
potential is the sum of an arbitrary function and the square of the function
integral, and models in which the potential is the sum of an arbitrary function
and the derivative of its square root, respectively. The cosmological
properties of all models are investigated in detail, and it is shown that they
can describe the inflationary or the late accelerating phase in the evolution
of the Universe
