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By analyzing the large-angle Bhabha scattering events e+e− → (γ)e+e− and diphoton events e+e− → (γ)γγ for the data sets collected at center-of-mass (c.m.) energies between 2.2324 and 4.5900 GeV (131 energy points in total) with the upgraded Beijing Spectrometer (BESIII) at the Beijing Electron-Positron Collider (BEPCII), the integrated luminosities have been measured at the different c.m. energies, individually. The results are important inputs for the R value and J/ψ resonance parameter measurements.