Question: dsolve/numeric and numerical functions

Int(exp(t), t= 0 ..x) +1 is just a way to write exp(x), use value(%).

ff:= x -> evalf(Int(exp(t), t= 0 .. x, method = _d01ajc) + 1) does
the same, but in a numerical way.

Now consider that as a differential equation, to be solved numerically:

de:=D(f)(x) = f(x);
dsolve({%, f(0)=1});
                         f(x) = exp(x)


ff:= x -> evalf(Int(exp(t), t= 0 .. x, method = _d01ajc) + 1);

D(f)(x) = ff(x);
sol:=dsolve({%, f(0)=1}, numeric);

  Warning, The use of global variables in numerical ODE problems is deprecated,
  and will be removed in a future release. Use the 'parameters' argument instead
  (see ?dsolve,numeric,parameters)

sol(1);

  Error, (in sol) parameter 't' must be assigned a numeric value before
  obtaining a solution

Question: how to write it down correctly?