The PROFIL and PROFIL-2 experiments were carried out in the fast reactor PHENIX. They were designed to provide integral information on neutron cross sections [(n,γ), (n,2n), and (n,f)] of several fission products and actinides. Previous interpretations report integral results with unrealistic small uncertainties that only take into account the statistical contribution. This work presents an uncertainty propagation technique able to include systematic uncertainties due to neutron fluence scaling. Such a technique consists of marginalizing analytically the uncertainties of the nuclear data (nuisance parameters) involved in the fluence scaling procedure. For the capture cross sections of 235U, 238U, and 239Pu, the interpretation of the PROFIL and PROFIL-2 experiments with the international library JEFF-3.1.1 provides excellent C/E results equal to 1.000, 1.019, and 0.982, respectively, with a relative uncertainty close to 1.5% (1σ).