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. But I'm now going to define a new function based on a definite integral of f of t. Let's define our new function. Let's say g, let's call it g of x. Let's make it equal to the definite integral from negative two to x of f of t dt.