I find Postman is great for API testing during development, but is there any tool for automating API integration testing as part of a CI setup?

Of course such a tool would probably need to work within the corporate firewall in order to access dev endpoints, perhaps also be able to interrogate internal DBs to verify data correctness. And of course automatically running tests and reporting/failing builds if desired post-build.

I will build a tool that does this if:

a) Such tool doesn't already exist.

b) There are enough comments here to suggest demand from people willing to pay for this.