Definite Integrals - Part 1

If F(x) is the antiderivative of a function f(x) continuous on (a,b)which means F'(x) = f(x) (a
∫f(x)dx {from a to b} = F(x) from a to b = F(b) - F(a)


Definite integral - Geometrical interpretation

the definite integral represents the algebraic sum of the areas of the figures bounded by

the graph of the function y = f(x)
the x axis
the straight line x =a and x = b.

if the curve goes above and below the x axis in the interval a to b, the areas of above the x axis enter this sum with a plus sign, while those below the x axis enter it with a minus sign.


Good online material

http://tutorial.math.lamar.edu/Classes/CalcI/DefnofDefiniteIntegral.aspx