  The aim of this work is to revisit viscosity solutions' theory for
second-order elliptic integro-differential equations and to provide a general
framework which takes into account solutions with arbitrary growth at infinity.
Our main contribution is a new Jensen-Ishii's Lemma for integro-differential
equations, which is stated for solutions with no restriction on their growth at
infinity. The proof of this result, which is of course a key ingredient to
prove comparison principles, relies on a new definition of viscosity solution
for integro-differential equation (equivalent to the two classical ones) which
combines the approach with test-functions and sub-superjets.
