Question regarding integration when adding a constant to the limits

Questions
1

I have to show that if f is continuous in the interval [a,b] were λ≠0 is a constant, that we have the following;

SeKhE.png

The task is hinting that i need to use integration by substitution.

Im lost.. Please help.

SeKhE.png

2

I would do it this way, but the result is incomprehensible:

IntegrateChangeVariables[
 Inactive[Integrate][
  f[x - \[Lambda]], {x, a + \[Lambda], b + \[Lambda]}],
 t, t == x - \[Lambda]]
3

What a strange result, indeed - maybe a bug? For case (b) the result is as expected:

Refine[IntegrateChangeVariables[
   Integrate[f[x/\[Lambda]], {x, a \[Lambda], b \[Lambda]}], t, t == x/\[Lambda]], \[Lambda] > 0] /. t -> x