So, I'm really rusty with math and I have a question that is stumping me. It's making me really mad because I'm sure somewhere in the back of my mind I know how to do it, but I can't figure it out. Here is the question:

I will denote: squared as (f)^2 and integrals as int[function]. all integrals go from a to b and f''(x) = second derivative of f

Verify that for f,g in R:

int[f''(x)^2] dx - int[g''(x)^2] dx = int[(f''(x)-g''(x))^2] dx + 2 int[g''(x)(f''(x)-g''(x))]dx

I'd really appreciate some help or ideas, I'm pretty sure there is a way to do it without trying to solve the integral, and all i have to do is verify the result. thanks!