Context :

Aims : We aim to measure the physical properties of the hot X-ray corona of two active galactic nuclei , NGC 4388 and NGC 2110 .

Methods : We analysed the hard X-ray ( 20–300 keV ) INTEGRAL spectrum in conjunction with archival XMM–Newton and NuSTAR data .

Results : The X-ray spectrum of both sources is phenomenologically well described by an absorbed cut-off power law .
In agreement with previous results , we find no evidence of a Compton reflection component in these sources .
We obtain a high-energy cut-off of 200 ^ { +75 } _ { -40 } keV for NGC 4388 and 320 ^ { +100 } _ { -60 } keV for NGC 2110 .
A fit with a thermal Comptonisation model yields a coronal temperature of 80 ^ { +40 } _ { -20 } keV and 75 ^ { +20 } _ { -15 } keV , respectively , and an optical depth of approximately two , assuming a spherical geometry .
The coronal temperature and luminosity of both sources are consistent with pair production that acts as a thermostat for the thermal plasma .
These results emphasise the importance of good signal-to-noise X-ray data above 100 keV to probe the high-energy emission of AGNs .

Conclusions :