  In this paper, we classify the irreducible integrable modules with finite
dimensional weight spaces and non-trivial $\widetilde{\mathfrak g}_c$-action
for the nullity $2$ toroidal extended affine Lie algebra $\widetilde{\mathfrak
g}$, where $\widetilde{\mathfrak g}_c$ is the core of $\widetilde{\mathfrak
g}$.
