A hash function does not provides integrity! last month
Some of you might have seen the answer of this famous stack overflow question what are the differences between a digital signature, a mac and a hash?:
The above table is from the most upvoted answer --but it is false. A hash function does not provide integrity, a MAC provides integrity.
Instead a cryptographic hash function provides three properties, well defined in the world of cryptography: collision resistance, pre-image resistance and second pre-image resistance. Nothing else.