Question: Extracting 'f(x)' from Int(f(x), x=0..1).

Sorry for the bad format, maple input is not working.

In particular,from an expression, something like

 Int(x*f(x), x = 0 .. 1)+ Int(x, x = 0 .. 1/3)+3* Int(x*f(x), x = 0 .. 2/3)

I want to extract 

x*f(x)+x+3*x*f(x)

That is all the integrands occuring in the expression. GetIntegrand helps to find the integrand but only for one integral, how do I do it for an expression like above.

I tried to apply following approach

subs(sin(c::anything)=c, sin(x)+f);

and the output was

f

I was expecting to get only 'x+f' for output.

EDIT 1: 

Thank you so much for your help. You guys answered exactly what I asked for. I needed this to do something different but I should have been more careful. I realized, I could not get that part now. This is what I actually need to do, if

A:=-(5/8)*x*(Int(f(x), x = 0 .. x))+(5/24)*(Int(f(x), x = 1/3 .. x))-(1/4)*x*(Int(x*f(x), x = 1/3 .. x));

then I wish to get a function, g(xi),

g(xi)= -(5/8)x*f(xi) ;   if 0<= xi <= x
                                                  (5/24)*f(xi)-(1/4)*x*xi*f(xi) ; if 1/3<= xi<= x

Notice, all the terms after integral should use variable 'xi' and terms occurring before integral remains as it is.