  We present a new method for computing multi-loop scattering amplitudes in
Quantum Field Theory. It extends the Generalized Unitarity method by
constraining not only the integrand of the amplitude but also its full
integrated form. Our approach exploits the relation between cuts and
discontinuities of the amplitude. Explicitly, by the virtue of analyticity and
unitarity of the S-matrix, the amplitude can be expressed in terms of
lower-loop on-shell amplitudes dispersively integrated along cuts. As both cuts
and discontinuities can be computed systematically in dimensional
regularization, we validated our method by reproducing the four-gluon amplitude
in two-loop massless Quantum Chromodynamics. Moreover, since our approach
improves the performance of the calculation, we provide a new result for the
four-loop four-point massless planar ladder Feynman integral. It is expressed
in terms of Harmonic Polylogarithms with letters 0 and 1.
