All of the observations performed with the IBIS telescope onboard the INTEGRAL observatory during the first one and a half years of its in-orbit operation (from February 10, 2003, through July 2, 2004) have been analyzed to find X-ray bursts. IBIS/ISGRI detector lightcurves total count rate in the energy range 15-25 keV revealed 1077 bursts of durations from ~5 to ~500 s detected with a high statistical significance (only one event over the entire period of observations could be detected by a chance with a probability of 20%). Apart from the events associated with cosmic gamma-ray bursts (detected in the field of view or passed through the IBIS shield), solar flares, and activity of the soft gamma repeater SGR1806-20, we were able to localize 105 bursts and, with one exception, to identify them with previously known persistent or transient X-ray sources (96 were identified with known X-ray bursters). In one case, the burst source was a new burster in a low state. We named it IGR J17364-2711. Basic parameters of the localized bursts and their identifications are presented in the catalog of bursts. Curiously enough, 61 bursts were detected from one X-ray burster - GX 354-0. The statistical distributions of bursts in duration, maximum flux, and recurrence time have been analyzed for this source. Some of the bursts observed with the IBIS/ISGRI telescope were also detected by the JEM-X telescope onboard the INTEGRAL observatory in the standard X-ray energy range 3-20 keV.
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