Context :

Aims : We present INTEGRAL light curves and spectra of the black-hole binary Cyg X-1 during a bright event that occurred in 2006 September , and which was simultaneous with a detection at 0.15–1 TeV energies by the MAGIC telescope .

Methods : We analyse the hard X-ray emission from 18 to 700 keV with the INTEGRAL data taken on 2006 September 24–26 by the IBIS and SPI instruments .
These data are supplemented with RXTE All Sky Monitor data at lower energy .
We present the light curves and fit the high energy spectrum with various spectral models .

Results : Despite variations in the flux by a factor of \sim 2 in the the 20–700 keV energy band , the shape of the energy spectrum remained remarkably stable .
It is very well represented by an e-folded power law with the photon index of \Gamma \simeq 1.4 and a high energy cut-off at E _ { c } \simeq 130 –140 keV .
The spectrum is also well described by thermal Comptonisation including a moderate reflection component , with the solid angle of the reflector of \sim 0.4 \times 2 \pi .
The temperature of the hot Comptonising electrons is kT _ { e } \sim 70 keV and their Thomson optical depth is \tau \sim 2.5 .
These spectral properties are typical of those observed in the low/hard state .
This shows that Cyg X-1 may stay in the low hard state at least up to the flux level of 2 Crab , which corresponds to \sim 2–3 % of the Eddington luminosity .
It is the first time a persistent high-mass black-hole binary is observed at a few percent of the Eddington luminosity with a stable low/hard state spectrum over a period of a few days .
Such a bright hard state has so far been observed only during the rising phase of transient low-mass black-hole binaries .
The TeV detection coincides with the peak of a small X-ray flare just after a very fast rise in hard X-ray flux .
In contrast , the source remained undetected by MAGIC at the peak of a larger X-ray flare occurring one day later and corresponding to the maximum of the X-ray luminosity of the whole outburst .
We do not find any obvious correlation between the X-ray and TeV emission .

Conclusions :