>>10563830i can explain both to you in about a minute. im going to call g(x) the derivative of f(x) for both explanations
the derivative of a function, f(x), is another function, g(x), which gives you the slope at every x of f(x). for example, if you plug 3 into f(x) and get 5 and then you plug in 3 into g(x) and get 2, this means that the slope at (3,5) is 2
the definite integral of a function, g(x), will give you the area under a curve between *two points*. this area corresponds to the difference in outputs when you plug in the *two points* into the indefinite integral of g(x). for example, if i take the definite integral of g(x) from 1 to 5 and I get 7.5, this means that the indefinite integral (aka the function that, when I take the derivative of it, it gives me g(x) ) of g(x) is a function that, if i plug in 1 and 5 and then take the difference of the two outputs i will get 7.5... in other words, if you plug in *two x-values* in f(x) you will get two y-values. if you take the integral of g(x) between those same x-values you will get an area equal to the difference of those y-values
