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[tex] \lim_{r \to \infty} \int_{-1}^1 dt f(t) e^{i r (t-1)} [/tex]

for some function [itex]f(t)[/itex]. I don't know what the exact form of [itex]f(t)[/itex] 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.

How should I go about this?

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