  To study the nature of the state $Y(2175)$, a dedicated data set of $e^+e^-$
collision data was collected at the center-of-mass energy of 2.125 GeV with the
BESIII detector at the BEPCII collider. By analyzing large-angle Bhabha
scattering events, the integrated luminosity of this data set is determined to
be $108.49\pm0.02\pm0.85$ pb$^{-1}$, where the first uncertainty is statistical
and the second one is systematic. In addition, the center-of-mass energy of the
data set is determined with radiative dimuon events to be
$2126.55\pm0.03\pm0.85$ MeV, where the first uncertainty is statistical and the
second one is systematic.
