It is good to hear that you did not encounter any issues running Integrity 10.4 on a CentOS 6.7 platform. I myself am employing a test system on CentOS 7 since some time, and have never had any trouble either.
However, I would want to make you aware that this has never been a supported platform for Integrity - as is the case with CentOS 6.10. You can find the supported platforms via this article.
I'd also recommend you review the product calendar you can find a link to in the given article - as support for Integrity 10.4 is no longer available. You might want to consider upgrading to a later version in order to benefit from the latest fixes and features.
If you choose to remain on your Integrity version and platforms, I can but advise you to compile and perform the test cases yourself. I do not expect any issues from your planned upgrade, but it will not be compliant.