  We study the integrability of polynomial vector fields using Galois theory of
linear differential equations when the associated foliations is reduced to a
Riccati type foliation. In particular we obtain integrability results for some
families of quadratic vector fields, Li\'enard equations and equations related
with special functions such as Hypergeometric and Heun ones. The Poincar\'e
problem for some families is also approached.
