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Context. We present rotation period measurements for subgiants observed by CoRoT. Interpreting the modulation of stellar light that is caused by star-spots on the time scale of the rotational period depends on knowing the fundamental stellar parameters. Aims. Constraints on the angular momentum distribution can be extracted from the true stellar rotational period. By using models with an internal angular momentum distribution and comparing these with measurements of rotation periods of subgiant stars we investigate the agreement between theoretical predictions and observational results. With this comparison we can also reduce the global stellar parameter space compatible with the rotational period measurements from subgiant light curves. We can prove that an evolution assuming solid body rotation is incompatible with the direct measurement of the rotational periods of subgiant stars. Methods. Measuring the rotation periods relies on two different periodogram procedures, the Lomb-Scargle algorithm and the Plavchan periodogram. Angular momentum evolution models were computed to give us the expected rotation periods for subgiants, which we compared with measured rotational periods. Results. We find evidence of a sinusoidal signal that is compatible in terms of both phase and amplitude with rotational modulation. Rotation periods were directly measured from light curves for 30 subgiant stars and indicate a range of 30 to 100 d for their rotational periods. Conclusions. Our models reproduce the rotational periods obtained from CoRoT light curves. These new measurements of rotation periods and stellar models probe the non-rigid rotation of subgiant stars. [ABSTRACT FROM AUTHOR]