# Large $r$ limit of integral

## Main Question or Discussion Point

I am doing some calculation and am now stuck with an integral of the form

$$\lim_{r \to \infty} \int_{-1}^1 dt f(t) e^{i r (t-1)}$$

for some function $f(t)$. I don't know what the exact form of $f(t)$ is.

Is there any way to address this integral? Similar to the saddle-point method perhaps? The saddle-point method does not work here right? since the argument of the exponential does not have a minima.

Can we say that this integral is dominated by a certain value of $t$, say at $t=1$? Why or why not?