  In this work, we construct a new general two-point quadratre rules for the
Riemann--Stieltjes integral $\int_a^b {f\left( t \right)du\left( t \right)}$,
where the integrand $f$ is assumed to be satisfied with the H\"{o}lder
condition on $[a,b]$ and the integrator $u$ is of bounded variation on $[a,b]$.
The dual formulas under the same assumption are proved. Some sharp error
$L^p$--Error estimates for the proposed quadrature rules are also obtained.
