What do we call the $\alpha$ in Riemann Integral?

Question

I am learning the concept of Riemann Integral.

$F(x) \text{ sometimes denoted as} \int_a^xfd\alpha$.

What I know is $\alpha$ is a function which maps $x\mapsto\Bbb R$(Is this domain and codomain correct?)

But I want to know with which term we call this $\alpha$

Answer 1

If this is a Riemann-Stieltjes integral, then $\alpha$ is called the integrator.