By exploiting the nanometer sensitivity of the confocal response to the position of an in-focus reflecting surface, we measured the bending rigidity of lipid-bilayer vesicles with a noninvasive all-optical method. The vesicles were weakly deformed with femtonewton optical force, and the bending rigidity was measured continuously from the L(alpha) through the P(beta(')) to the L(beta(')) phases on the same specimen for the first time. The bending modulus is found to increase by an order of magnitude from the L(alpha) phase to the L(beta(')) phase, as a result of the increasing area-compressibility modulus and bilayer thickness. The dips of bending modulus give precisely the main-transition and pretransition temperatures, which supports the recently proposed chain-melting model of pretransition.