  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 and digamma events, we measure the integrated
luminosity of the data sample to be ($496.3 \pm 0.3 \pm 3.0$)~pb$^{-1}$, where
the first uncertainty is statistical and the second is systematic. This work
provides a basis for future luminosity measurements at Belle~II.
