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

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()?