Remark The value of the definite integral of a function over any particular interval
depends on the function and the interval, but not on the variable of integration that we
INTEGRALS         333
choose to represent the independent variable 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