  Singularities hidden in the collinear region around an external massless leg
may lead to conformal symmetry breaking in otherwise conformally invariant
finite loop momentum integrals. For an $\ell$-loop integral, this mechanism
leads to a set of linear $2$nd-order differential equations with a
non-homogeneous part. The latter, due to the contact nature of the anomaly in
momentum space, is determined by $(\ell-1)$-loop information. Solving such
differential equations in general is an open problem. In the case of 5-particle
amplitudes up to two loops, the function space is known, and we can thus follow
a bootstrap approach to write down the solution. As a first application of this
method, we bootstrap the 6D penta-box integral.
