  We investigate the cross-correlation between the cosmic infrared background
(CIB) and cosmic microwave background (CMB) anisotropies due to the integrated
Sachs-Wolfe (ISW) effect. We first describe the CIB anisotropies using a
linearly biased power spectrum, valid on the angular scales of interest. From
this, we derive the theoretical angular power spectrum of the CMB-CIB
cross-correlation for different instruments and frequencies. Our cross-spectra
show similarities in shape with usual CMB/galaxies cross-correlations. We
discuss the detectability of the ISW signal by performing a signal-to-noise
(SNR) analysis with our predicted spectra. Our results show that : (i) in the
ideal case of noiseless, full-sky maps, the significances obtained range from 6
to 7 sigmas depending on the frequency, with a maximum at 353 GHz (ii) in
realistic cases which account for the presence of noise including astrophysical
contaminents, the results depend strongly on the major contribution to the
noise term. They span from 2 to 5 sigmas, the most favorable frequency for
detection being 545 GHz. We also find that the joint use of all available
frequencies in the cross-correlation does not improve significantly the total
SNR, due to the high level of correlation of the CIB maps at different
frequencies.
