Symbolically, we write
limSn
n→∞
 = lim
n
n
s
→∞
 = area of the region PRSQP = 
( )
b
∫a f x dx (5)
It follows that this area is also the limiting value of any area which is between that
of the rectangles below the curve and that of the rectangles above the curve For
the sake of convenience, we shall take rectangles with height equal to that of the
curve at the left hand edge of each subinterval Thus, we rewrite (5) as
( )
b
∫a f x dx
 =
lim0
[ ( )
(
)