  Recently, Rosengren utilized an integral method to prove a number of
conjectural identities found by Kanade and Russell. Using this integral method,
we give new proofs to some double sum identities of Rogers-Ramanujan type.
These identities were earlier proved by approaches such as combinatorial
arguments or by using $q$-difference equations. Our proofs are based on
streamlined calculations, which relate these double sum identities to some
known Rogers-Ramanujan type identities with single sums. Moreover, we prove a
conjectural identity of Andrews and Uncu which was earlier confirmed by Chern.
