  We explore the idea to bootstrap Feynman integrals using integrability. In
particular, we put the recently discovered Yangian symmetry of conformal
Feynman integrals to work. As a prototypical example we demonstrate that the
D-dimensional box integral with generic propagator powers is completely fixed
by its symmetries to be a particular linear combination of Appell
hypergeometric functions. In this context the Bloch-Wigner function arises as a
special Yangian invariant in 4D. The bootstrap procedure for the box integral
is naturally structured in algorithmic form. We then discuss the Yangian
constraints for the six-point double box integral as well as for the related
hexagon. For the latter we argue that the constraints are solved by a set of
generalized Lauricella functions and we comment on complications in identifying
the integral as a certain linear combination of these. Finally, we elaborate on
the close relation to the Mellin-Barnes technique and argue that it generates
Yangian invariants as sums of residues.
