7 1  Definite integral as the limit of a sum
Let f be a continuous function defined on close interval [a, b] Assume that all the
values taken by the function are non negative, so the graph of the function is a curve
above the x-axis The definite integral 
( )
b
∫a f x dx
 is the area bounded by the curve y = f (x), the
ordinates x = a, x = b and the x-axis