Divide the area under the curve into an even number of equally spaced intervals along the x axis. If you want to find the area under the curve from 0 to 8, for example, you might divide the area into four intervals, each having a width of two in the x direction.
Subtract the lower limit of x from the higher limit of x and divide the result by the number of intervals. For an area from 0 to 8 divided into four intervals, use the equation (8 - 0)/4 = 2.
Divide the result by three -- in this example, you would get 2/3. Record this number for later use.
Calculate the value of f(x) at each division along the curve, starting with the lower limit and ending with the upper limit. For a curve from 0 to 8 divided into four intervals, calculate the values of f(x) at 0, 2, 4, 6 and 8. If the equation of the curve is f(x) = x^2 - x + 2, for example, calculate f(0) = 2, f(2) = 4, f(4) = 14, f(6) = 32 and f(8) = 58.
Multiply the second value of f(x) by 4. Multiply the third value of f(x) by 2. Continue multiplying with this pattern until you reach the next-to-last value of f(x), which should be multiplied by 4. Add all the values together; for example, f(0) + 4*f(2) + 2*f(4) + 4*f(6) + f(8) = 2 + 4*4 + 2*14 + 4*32 + 58 = 168.
Multiply the result of step 5 by the result of step 3. For example, (2/3)*168 = 112. This result approximates the area under the curve.