  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, Romer, 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 and HETE-2 would detect a higher number of GRBs than
INTEGRAL (~8 and ~22 more detections than IBIS and JEM-X respectively),
INTEGRAL and specially IBIS would detect very high redshift (z > 15) GRBs,
unreachable for Swift and HETE-2. This fact is very relevant for studying a
population of GRBs further than z=15, which would be associated with the
population III of stars. Therefore, the INTEGRAL mission (precisely IBIS) will
be a very valuable tool to trace the primitive star formation rate at the early
universe.
