MHB How Large Can This Integral Be?

[DaalChawal]

 

[Opalg]

$|\cos(2017\theta)|\leqslant1$.

$|5-4\cos\theta|\geqslant1$.

Use those facts to estimate how large $\displaystyle\left|\int_0^\pi\frac{\cos(2017\theta)}{5-4\cos\theta}d\theta\right|$ can be. Then decide which of the four given choices seems most likely to be correct.