Integral attacks exploit structural weaknesses in symmetric cryptographic primitives by analyzing how subsets of inputs propagate to produce outputs with specific algebraic properties. For the case of (XOR) key-alternating block ciphers using (independent) round keys, at ASIACRYPT’21, Hebborn et al. established the first non-trivial lower bounds on the number of rounds required for ensuring integral resistance in a quite general sense. For the case of adding keys by modular addition, no security arguments are known so far. Here, we present a unified framework for analyzing the integral resistance of primitives using (word-wise) modular addition for key whitening, allowing us to not only fill the gap for security arguments, but also to overcome the heavy computational cost inherent in the case of XOR-whitening.