You could have something defined like this. F of x is equal to x squared if x odd, and you could say it's equal to x to the third otherwise. So if it's an odd integer, it's an odd integer, you just square it, but otherwise for any other real number, you take it to the third power. This is a valid way of defining a function. What we're going to do in this video is explore a new way, or a potentially new way for you, of defining a function, and that's by using a definite integral, but it's the same general idea. So what we have graphed here, this is the t-axis, this is the y-axis, and we have the graph of the function f, or you could view this as the graph of y is equal to f of t. Now what I want, and this is another way of representing what outputs you might get for a given input here if t is one, f of t is five. If t is four, f of t is three.