Are all functionals integrals?

Q: Are all functionals integrals?

A: Yes.

As long as we're working within a complete inner product space (that is, a Hilbert Space) with an inner product defined by (f,g)=∫Kf(x)g(x)dx(f,g)=∫Kf(x)g(x)dx, the Riesz representation theorem allows us to conclude that "all functionals are integrals". – Omnomnomnom Sep 9 '14 at 4:26

Source:

http://math.stackexchange.com/questions/924427/are-all-definite-integrals-considered-functionals