(
( –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)
( )
( ) (
)]
n
n
f
f
f
f
n
n
n
n
→∞
+
+
+
+
=
2
2
2
2
2
2
1
2
4
(2 – 2)
2 lim
[1
(
1)
(
1) 1 ]
n
n
n
n
n
n
→∞


+
+
+
+
+
+
+




=
2
2
2
-
1
1
2 lim
[(1 1 1)
(2
4