silly question.... are the integrals: [tex]\int_a^{b}dnf(t,n)[r(n+g(n] [/tex] and [tex]\int_a^{b}dnf(t,n)r(n)+\int_a^{b}dkf(t,k)g(k) [/tex] the same?..i know that n and k are dummy variable so we can always make the change of variable k=n or n=k inside one of the two integral...
You seem to have lost a couple of right parentheses. If you meant: [tex]\int_a^{b}dnf(t,n)[r(n)+g(n)] [/tex] Yes, they are exactly the same.
A technicality: [itex]\int f + g = \int f + \int g[/itex] provided the two integrals on the right hand side exist. (Knowing the left hand side exists is not enough)