Deriving Phase Response from Group Delay

Hi, I am trying to derive Phase response from group delays. Assume I have a constant group delay of 1 second for all frequencies then I can determine the phase response to be: phase(f)=C - 2*pi* integral(tau df) where tau is the delay of 1 second. How do I determine the constant C?

Is there any other way to determine phase response given group delay?

Another question I have is that for a filter that gives non linear phase response phase delay and group delay are generally different while for linear phase response group delay and phase delay are equal to each other. Which one is used to derive non linear phase response? Group delay or Phase delay?

Thank you in advance.