  Rota-Baxter operators are an algebraic abstraction of integration. Following
this classical connection, we study the relationship between Rota-Baxter
operators and integrals in the case of the polynomial algebra $\mathbf{k}[x]$.
We consider two classes of Rota-Baxter operators, monomial ones and injective
ones. For the first class, we apply averaging operators to determine monomial
Rota-Baxter operators. For the second class, we make use of the double product
on Rota-Baxter algebras.
