  The structure of hadrons relevant for deep-inelastic scattering are
completely characterised by the Compton amplitude. A direct calculation of the
Compton amplitude in a lattice QCD setup provides a way to accessing the
structure functions, circumventing the operator mixing and renormalisation
issues of the standard operator product expansion approach. In this
contribution, we focus on the QCDSF/UKQCD Collaboration's advances in
calculating the forward Compton amplitude via an implementation of the
second-order Feynman-Hellmann theorem. We highlight our progress in
investigating the moments of nucleon structure functions.
