How Does Using Midpoints in Integrals Estimate Area?

[moaath]

1. let A be the area of the region that lies
under the graph of f(x) = e^-x , between x=0 and x=2.

1-Estimate the area using the sample point to be the midpoint and using fuor sub-intervals.
x*1=(0+0.5)\2=1\4.
x*2=(1+0.5)\2=3\4.
x*3=(1+3\2)\2=5\4.
x*4=(2+3\2)\2=7\4
A=segma i=1 to n f(x*i) X delta x =0.8357

I copied the answer from the board with my doctor but I didn't understand the solution

 

[Mark44]

What part of the solution did you not understand?