  General relativity and supergravity become integrable systems after
dimensional reduction to two spacetime dimensions. This means the equations of
motion can be encoded in the flatness condition for a Lax operator. Nicolai and
Warner found Lax operators for dimensionally reduced supergravity. They gave
explicit formulas primarily for the case with $N=16$ supersymmetry in two
dimensions (which corresponds to $N=8$ supergravity in four dimensions). In
this note, we derive analogous results for the case with $N=2$ supersymmetry in
two dimensions (which corresponds to $N=1$ supergravity in four dimensions).
This is the simplest example of the general fact that supergravity becomes an
integrable system after dimensional reduction to two dimensions.
