Context : If relativistic particle acceleration takes place in colliding-wind binaries , hard X-rays and \gamma -rays are expected through inverse Compton emission , but to date these have never been unambiguously detected .

Aims : To detect this emission , observations of $ η $ ~Carinae were performed with INTEGRAL , leveraging its high spatial resolution .

Methods : Deep hard X-ray images of the region of $ η $ ~Car were constructed in several energy bands .

Results : The hard X-ray emission previously detected by BeppoSax around $ η $ ~Car originates from at least 3 different point sources .
The emission of $ η $ ~Car itself can be isolated for the first time , and its spectrum unambiguously analyzed .
The X-ray emission of $ η $ ~Car in the 22–100Â keV energy range is very hard ( \Gamma \simeq 1 \pm 0.4 ) and its luminosity is 7 \times 10 ^ { 33 } Â erg s ^ { -1 } .

Conclusions : The observed emission is in agreement with the predictions of inverse Compton models , and corresponds to about 0.1 % of the energy available in the wind collision . $ η $ ~Car is expected to be detected in the GeV energy range .