Can someone please give a very simplified explanation of Riemann Summs

I am taking calculus 1 online and the professor doesn't answer emails especially regarding how to do something. I have done okay (average score for the class) but just don't understand it.

I know what Riemann Sums find (the area under the curve) but I am so confused on how to find it except for on the calculator. How do I know how many rectangles to break it into?

Example:

(1-x^2)dx from -1 to 1

I know the answer (according to the calculator) is 1.33 but, when I split into 2 rectangles, then it turns into 2/2 which is 1. It all comes out to 1.

I know that this is easy for most but not for me. The book does not do well at explaining things either.

Can anyone please explain this concept clearer?