Hence, the variable of integration is called a dummy variable Example 25 Find 
2
0 (2
1)
x
dx
+
∫
 as the limit of a sum Solution By definition
( )
b
∫a f x dx
 =
( – ) lim1
[ ( )
(
) (
( –1) ],
n
b
a
f a
f a
h
f a
n
h
→∞n
+
+
+
+
+
where,
h =
b–
a
n
In this example, a = 0, b = 2, f (x) = x2 + 1, 
2 – 0
2
h
n
n
=
=
Therefore,
2
2
0 (
1)
x
dx
+
∫
 =  
1
2
4
2 ( –1)
2 lim
[ (0)
( )
( )