Lecture 16 : Integral as a limit of Riemann sums [Section 16.2]
(ii)
To define Riemann sums for a function , we do not require to be bounded. However, it can be
proved that, if is integrable, then is also bounded.
16.2.4
Example:
Let
We know that is a continuous function, and hence it is integrable. To compute its integral, for every , consider the partition obtained by dividing into equal parts, i.e., .
Note that,
, we do not require 
to be bounded. However, it can be 
is integrable, then 
is also bounded. 
is a continuous function, and hence it is integrable. To compute its integral, for every 
, consider the partition 
obtained by dividing 
into 
equal parts, i.e., 
.
. Then, 
