Note that

in the given closed interval, so the area is exactly given by the definite integral

(no absolute values needed!)
Integrating gives
Ok sure—————-_______—-____
In 2 2/3 months you ran 76 miles.
To know how many miles you ran each month, you can simply use cross multiplication as follows:
number of miles per month= (76) / (2 2/3)
= 28.5 miles