Okay I have several questions that have been bothering me for some time now, so bear with me please. How does integration work? Integrating the function f(x) between the bounds a,b finds the area under f(x) between a and b. But how does this work? If my function is f(x) = 2x and my bounds are [1,10], how come F(10) - F(1) equals the area under 2x from 1,10? (Where F(x) = x^2). Furthermore, why does a derivative work? The derivative of the function f(x) yields a relationship between the rate of change in f(x) and a given input. But how does this actually work? Or put in a different way, if my function is 1x^2, why can I multiply the coefficient by the exponent to yield a function (2x) that tells me the rate at which the function will change? What does it mean that time is being removed (divided in a derivative) or added (multiplied in an integral)? Thanks for reading.