




We define the area under a curve formally as follows. This definition involves only the values of the integrand and does not presuppose any algebraic formula for it.
Step 1
Break the interval between a and b into n equal parts, each of width .
Step 2
Pick a point in the kth part.
Step 3
Estimate the area by the sum of the areas of the n rectangles:
If no matter how we choose , the sum converges to the same value, that value is the integral.
Any sum S_{n} of this form is called a Riemann sum.