  We calculate the four-point correlation function of half-BPS operators with
weights 2, 3, 3, 4 in N=4 SYM to two-loop order. The OPE of this correlation
function provides a nontrivial check of the integrability conjecture for a
class of three-point functions formulated in arXiv:1311.6404. Our perturbative
calculation exploits the supergraph formalism in N=2 harmonic superspace.
