  Rota-Baxter operators present a natural generalisation of integration by
parts formula for the integral operator. In 2015, Zheng, Guo, and Rosenkranz
conjectured that every injective Rota-Baxter operator of weight zero on the
polynomial algebra $\mathbb{R}[x]$ is a composition of the multiplication by a
nonzero polynomial and a formal integration at some point. We confirm this
conjecture over any field of characteristic zero. Moreover, we establish a
structure of an ind-variety on the moduli space of these operators and describe
an additive structure of generic modality two on it. Finally, we provide an
infinitely transitive action on codimension one subsets.
