The Big Ideas of Calculus I

The derivative of a function F at 2 is the limit of the difference quotient for F at 2, written , It measures the slope of the graph of at , the rate of change of at .
If we divide the interval into equal sub-intervals of size then is called the (Right) Riemann sum for the function over .
The integral of over is , the limit of the (Right) Riemann sums. It measures the difference in areas under/over the graph of over .

Fundamental Theorem of Calculus

If is continuous on then: 1) is an anti-derivative of on , i.e., on 2) If is any anti-derivative of on then