  Recently, Bern et al observed that a certain class of next-to-planar Feynman
integrals possess a bonus symmetry that is closely related to dual conformal
symmetry. It corresponds to a projection of the latter along a certain
lightlike direction. Previous studies were performed at the level of the loop
integrand, and a Ward identity for the integral was formulated. We investigate
the implications of the symmetry at the level of the integrated quantities. In
particular, we focus on the phenomenologically important case of five-particle
scattering. The symmetry simplifies the four-variable problem to a
three-variable one. In the context of the recently proposed space of pentagon
functions, the symmetry is much stronger. We find that it drastically reduces
the allowed function space, leading to a well-known space of three-variable
functions. Furthermore, we show how to use the symmetry in the presence of
infrared divergences, where one obtains an anomalous Ward identity. We verify
that the Ward identity is satisfied by the leading and subleading poles of
several nontrivial five-particle integrals. Finally, we present examples of
integrals that possess both ordinary and dual conformal symmetry.
