Integral cryptanalysis is an effective method of block cipher analysis, and the integral distinguisher is usually constructed using a zero-sum property of some positions in the ciphertext. Based on the theorem of higher-order differential attack, the order of plaintexts can be exploited, to determine if some positions of the ciphertext are balanced. Inspired by the conventional integral cryptanalysis, the influence of constant on the leading-coefficient of polynomial is considered and the construction of probability integral distinguisher as well as the attack method are proposed in this study. When applied to PUFFIN, a 7-round probability integral distinguisher is constructed and used to mount a 9-round attack, and this attack can recover 92-bit round key. The data/time complexity is 2^24.8 chosen plaintexts, and 2^35.48 9 round encryptions, and the space complexity is 2²⁰.