Show that the given limit is a definite integral for a suitable interval and function

The limit is:

That's the problem I can't solve. Here is how far I've made it:

Since a definite integral can be defined as

Then:

which simplifies to:

I'm not sure how to solve, but, I can guess that which would simplify things to:

I can also guess that so that:

Now, I can't find a function that satisfies this. almost works but not quite.