The cosine varies between -1 and 1, so the square, being non-negative, varies between 0 and 1. Nowdothe plug-n-chug:

If you take the lower limit, then (exponential stuff)*(cosine stuff) is bounded below by (exponential stuff)*(zero), or zero.

If you take the upper limit, then (exponential stuff)*cosine stuff) is bounded above by (exponential stuff)*(one), or one.

If you're dealing with the lower limit, the expression simplifies as 0 + x + 1 = x + 1.

If you're dealing with the upper limit, the expression simplified as (e^x - x - 1) + x + 1 = e^x + x - x + 1 - 1 = e^x.