Integrated ferroelectric capacitors Pt/PZT/Pt/Ti/SiO2/Si with sol-gel deposited PZT films are studied. The (111) textured polycrystalline films are shown to have nonconductive PZT grain boundaries. The short-circuited photocurrents measured under illumination of the films by light with the quantum energy of 2.7 eV indicate the polarization inside the film directed from the top to the bottom electrode. Using the modified method of depolarization hysteresis loops, we found a non-switchable part of polarization which was measured to be -16 μC/cm2 and directed from the top to the bottom electrode. We consider this result to be a giant self-polarization and explain it in terms of flexoelectricity caused by lattice mismatch between the PZT and bottom Pt layers. The strain gradient across the PZT film thickness is estimated from the in-plane lattice constants measured in Pt and PZT films to be ∼103cm-1, which can produce the downward flexoelectric polarization of ∼14 μC/cm2, coinciding well with the measured one. Nonsymmetrical depolarization loops are found in the films when the polarization switching itself becomes more difficult under the negative or positive driving voltage. We show experimentally how depolarization with compensating bias or film illumination can affect the film polarization switching.