In this paper, we present a new cryptanalytic tool that can reduce the complexity of integral analysis against Addition-Rotation-XOR (ARX) based designs. Our technique is based on the partial-sum technique proposed by Ferguson et al. at FSE 2000, which guesses subkeys byte to byte in turn, and the data to be analyzed is compressed for each key guess. In this paper, the technique is extended to ARX based designs. Subkeys are guessed bit by bit, and the data is compressed with respect to the value of the guessed bit position and carry values to the next bit position. We call the technique bitwise partial-sum. We demonstrate this technique by applying it to reduced-round versions of HIGHT, which is one of the ISO standard 64-bit block ciphers. Another contribution of this paper is an independent improvement specific to HIGHT. By exploiting linear computations inside the round function, the number of guessed bits during the key recovery phase can be greatly reduced. Together with the bitwise partial-sum, the integral analysis on HIGHT is extended from previous 22 rounds to 26 rounds, while full HIGHT consists of 32 rounds.