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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 theBESIII detector at the BEPCII collider. By analyzing large-angle Bhabhascattering events, the integrated luminosity of this data set is determined tobe $108.49\pm0.02\pm0.85$ pb$^{-1}$, where the first uncertainty is statisticaland the second one is systematic. In addition, the center-of-mass energy of thedata set is determined with radiative dimuon events to be$2126.55\pm0.03\pm0.85$ MeV, where the first uncertainty is statistical and thesecond one is systematic.

Measurement of the integrated luminosity and the center-of-mass energy of the data taken by BESIII at $\sqrt{s} = 2.125$ GeV