I was revising my notes and I stumble across this problem. In my notes, it says that a feedback circuit required some feedback elements to works. Let's take the integrator op amp as example: The feedback mechanism used is negative feedback, right? So inside this circuit, are the feedback elements R1 and C2? Or is there no need for any "feedback elements" for a feedback circuit to work?
Feedback circuit or closed loop(as named in control theory) is used in control systems to know what happens in the output of system, and report that to the input and elaborate an input signal according to that!
So for your question the only element in the feedback is the capacitor. In the control community it is common to not use any feedback elements, but the wire is mandatory. It's called unit feedback.