If the independent variable is denoted by
t or u instead of x, we simply write the integral as 
( )
b
∫a f t dt
 or 
( )
b
∫a f u du
instead of
( )
b
∫a f x dx 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
[ ( )
(
)