The inequality is attributed to
P.L. Chebyshev, On approximate expressions of some integrals in terms of others, taken within the same limits, Proc. Math. Soc. Kharkov 2, 93–98 (1882).
more often cited with the title in French: "Sur les expressions approximatives des integrales definies par les autres prises entre les mêmes limites"
This article is online here, in Russian. I am having some difficulty to locate the inequality. The equation should be the one below, with $R_1\geq 0$, hopefully someone who reads Russian can locate that statement.
