Find the area between the two curves and vertical lines

The video tutorial explains how to sketch graphs of functions, specifically focusing on e^x and the identity function. It guides viewers through identifying the region of interest between x=0 and x=1, and calculating the area under the curve by integrating the difference between the functions. The tutorial concludes with simplifying the result and discussing the non-calculator approach.

How do you evaluate the integral of e^x from 0 to 1, and what is the result?

Describe the steps taken to simplify the expression for the area under the curve after integration.