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The integrated luminosities of the data samples collected in the BESIII experiment in 2016--2017 at center-of-mass energies between 4.19 and 4.28 GeV are measured with a precision better than 1% by analyzing large-angle Bhabha scattering events. The integrated luminosities of the old data sets collected in 2010--2014 are updated by considering correction related to the detector performance, offsettting the effect of newly discovered readout errors in the electromagnetic calorimeter that happen haphazardly.