MIBS is a lightweight block cipher which was proposed by Izadi et al. at CANS 2009. Its overall encryption structure uses the typical Feistel network, and the round function adopts the SP network. It supports both MIBS-64 and MIBS-80 versions, that is, it has 64-bit and 80-bit two key lengths with a 64-bit block size, and is suitable for strictly resource-constrained devices, such as low-cost RFID (radio frequency identification) tags. This paper researches the integral attack on the block cipher MIBS. Firstly, we observe the key schedules of MIBS-64 and MIBS-80, and find some properties between their round keys by using the automatic search algorithm for key-bridging technique, respectively. Secondly, using the bit-based division property and the automatic modeling search method based on MILP (mixed integer linear programming), we find some 8-round and 9-round integral distinguishers of MIBS. Finally, based on the 8-round integral distinguisher, we launch a 12-round key recovery attack for MIBS-64 with the data complexity \text2^\text60 , and the time complexity \text2^\text63\text.42 . Based on the 9-round integral distinguisher, we launch a 14-round key recovery attack for MIBS-80 with the data complexity \text2^\text63 , and the time complexity \text2^\text66 . These two key recoveries are the current best integral attacks on the block cipher MIBS-64 and MIBS-80.