By analyzing the large-angle Bhabha scattering events $e^+e^−$ $\rightarrow$ ($\gamma$)$e^+e^−$ and diphoton events $e^+e^−$ $\rightarrow$ ($\gamma$)$\gamma$ $\gamma$ 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/$\psi$ resonance parameter measurements.