How to use
Enter the function f (x) in the text input field marked "f(x)=".

 Example: f (x)=4-x2

Click the "Graph" button (this button also refreshes the graph).

Enter the endpoints of the interval [a,b] for the definite integral in the text input fields marked "a=" and "b=", and click the "Graph" button to refresh.

 Example: [a,b]=[-2,2]

Click the "+" and "-" buttons under the label marked "n=" to change the number of subintervals used for the approximation.

 Example: n=8

Adjust the slider to determine which point in each subinterval is used to determine the height of the rectangle, from left endpoint to right endpoint.

 Example: left endpoint

To erase the graph and all input fields, setting the slider to a default position and n to a default value, click the "Clear" button.


Examples
Polynomial:
f (x)=4-x2
[a,b]=[-2,2]
n=20 for both   
 left  mid  right

Exponential:
f (x)=e2
[a,b]=[0,2]
n=10 for both   
 left  mid  right

Trigonometric:
f (x) = sin x
[a,b]=[0,3.14159]
n=6 for both
 left  mid  right


Other Notes
The graph of f (x) is shown, with the rectangles over subintervals of [a,b] drawn in outline so that positive areas are green and negative areas are red. The approximate area computed is shown in the label marked "Area=".