Cleanness of overrings of polynomial rings

Let R be a commutative ring with identity. R is called clean (respectively, almost clean) if every element in R   is a sum of an idempotent and a unit (respectively, a regular element). In this paper, we clarify conditions under which the two overrings R(x)R(x) and R〈x〉R〈x〉 of the ring of polynomials R[x]R[x] are (almost) clean rings.