We discuss the INTEGRAL capabilities to detect a high redshift population of gamma-ray bursts (GRBs). First a simple comparison between other past or planned experiments (BATSE, SAX, HETE-2, Rømer, Swift) and INTEGRAL instrumentation (IBIS, JEM-X) is shown. After this first view we will be focused on comparing the capabilities of the two most sensitive missions (INTEGRAL/IBIS and Swift) of detecting a further population of GRBs. We conclude that, if the GRB rate is proportional to the star formation rate, the capabilities of studying GRBs of INTEGRAL are complementary to the ones of missions like Swift and HETE-2, specially devoted to prompt localizations of GRBs. Whereas Swift an
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