Estimating complex integral

[Brendy]

Homework Statement

I need to establish the estimate and inequality
$|\int_{C} e^{iz^{2}}dz| \leq\frac{\pi(1-e^{-R^{2}}}{4R} < \frac {\pi}{4R}$

where $C={z(t)=Re^{it},t\in[0,\fraq{\pi}{4}]$

Homework Equations

The Attempt at a Solution

I thought perhaps I could use the ML equality but the function doesn't have a global maximum. It does have a bound of 1 and -1 on the real and imaginary parts but using that as the maximum and then multiplying by the length does not give the inequality above.
I'm at a loss on how to do anything with this question. It's quite frustrating.