From April to July 2018, a data sample at the peak energy of the
$Upsilon(4S)$ resonance was collected with the Belle~II detector at the
SuperKEKB electron-positron collider. This is the first data sample of the
Belle~II experiment. Using Bhabha scattering events, we measure the integrated
luminosity of the data sample to be ($496.7 pm 0.3 pm 3.5$)~pb$^{-1}$, where
the first uncertainty is statistical and the second is systematic. A
measurement with digamma events is performed as a cross-check, and the obtained
result is in agreement with the nominal result. This work provides a basis for
future luminosity measurements at Belle~II.
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