Measurement of the integrated Luminosities of cross-section scan data samples around the (3770) mass regionSupported by National Key Basic Research Program of China (2015CB856700), National Natural Science Foundation of China (NSFC) (11235011, 11335008, 11425524, 11625523, 11635010), the Chinese Academy of Sciences (CAS) Large-Scale Scientific Facility Program, the CAS Center for Excellence in Particle Physics (CCEPP), Joint Large-Scale Scientific Facility Funds of the NSFC and CAS (U1332201, U1532257, U1532258), CAS Key Research Program of Frontier Sciences (QYZDJ-SSW-SLH003, QYZDJ-SSW-SLH040), 100 Talents Program of CAS, National 1000 Talents Program of China, INPAC and Shanghai Key Laboratory for Particle Physics and Cosmology, German Research Foundation DFG under Contracts Nos. Collaborative Research Center CRC 1044, FOR 2359, Istituto Nazionale di Fisica Nucleare, Italy, Koninklijke Nederlandse Akademie van Wetenschappen (KNAW) (530-4CDP03), Ministry of Development of Turkey (DPT2006K-120470), National Science and Technology fund, The Swedish Research Council, U. S. Department of Energy (DE-FG02-05ER41374, DE-SC-0010118, DE-SC-0010504, DE-SC-0012069), University of Groningen (RuG) and the Helmholtzzentrum fuer Schwerionenforschung GmbH (GSI), Darmstadt, WCU Program of National Research Foundation of Korea (R32-2008-000-10155-0)

To investigate the nature of the (3770) resonance and to measure the cross section for , a cross-section scan data sample, distributed among 41 center-of-mass energy points from 3.73 to 3.89 GeV, was taken with the BESIII detector operated at the BEPCII collider in the year 2010. By analyzing the large angle Bhabha scattering events, we measure the integrated luminosity of the data sample at each center-of-mass energy point. The total integrated luminosity of the data sample is , where the first uncertainty is statistical and the second systematic.