Functional derivatives

Showing the functional derivative of the integral of a two variable function is the same as the partial derivative of that function.

Seems kinda wrong, but I can't find a correct solution online so... going to go with what I got until someone tells me the right answer.

Quantum Field Theory for the Gifted Amateur. Ebook. Tom Lancaster, Stephen Blundell. New York, NY : Oxford University Press, 2014. 9780191779435 0191779431