How Can I Extract One Period of a Periodic Function that is Defined with Mod() ?

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Suppose I have a function, for example
syms t real
f(t) = triangularPulse(-1,1,t)
f(t) = 
Now create its periodic extension using mod()
P = 3;
f_P(t) = f(mod(t+1,P)-1); % Period = 3
fplot(f_P)
Suppose I want to integrate one period from f_P(t)
int(f_P(t),t,-1,-1+P)
ans = 
What I'm looking for is
int(f(t),t,-1,-1+P)
ans = 
1
But I can't figure out how to extract one period from f_P(t) in a form that int() can handle, which presumably would be an integrand not defined in terms of mod(). For example, I was hoping this might work
simplify(f_P(t)*rectangularPulse(-1,-1+P,t),100)
ans = 
Is there a way to define a symfun that is one period of f_P and is not defined in terms of mod()?

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