need help about op-amp theory

I have 2 op-amp figure.(attached in the word document)
I am wondering how is the Rf affect the output..
For more details about the question, please open the document.
thank you.

I am really appreciate your help.

Rf causes the output to deviate from "ideal" function of an integrator. I beileive this is called a "lossy" integrator. The reason to use it is to prevent the output from driving to the rail when the input is stady-state.