Strange output of Maxima in the laplace command for a wrong input: a semi-bug?

Dear Colleagues,

Please, forgive me with my inexperience with Maxima so far. I try to 
get improved with time.

I have been so careless as to give to Maxima the following incorrect
input:

laplace(integrate(f(x), x), x, s);

and I took the following strange reply to this incorrect input:

'integrate(laplace(f(x), x, s), x)

The input has been incorrect, since the indefinite integral of a function
f(x) contains an arbitrary constant C and this has not been taken into
account by me.

In any case, this output may lead to incorrect results. For example,
since for f(x)=cos(x)

integrate(cos(x), x)   gives   sin(x)

one (not Maxima of course) might conclude that the Laplace 
transform of sin(x) could be

'integrate(laplace(cos(x), x, s), x) i.e. integrate(s/(s^2+1), x) i.e. 
sx/(s^2+1) although it is simply 1/(s^2+1) as Maxima itself gives
even with the (so strange) command

laplace(integrate(cos(x), x), x, s);

In this way, one can further conclude that sx/(s^2+1) = 1/(s^2+1)
i.e. that sx = 1 for all values of s and x.

Concluding, my wrong input (my having neglected the integration
constant C) should not permit Maxima to interchange the order
of Laplace transformation and integration. This should be modified
in my opinion. (Mathematica and Maple do not proceed to this
interchange under a similar command; only Maxima does: versions
5.5 beta and 5.9.0 I have tested.)

I would greatly appreciate your comments on this situation and
I cannot exclude I have not understood what exactly happens with
Maxima. My first impression is that this might be a strange kind
of bug, and this should be corrected (even for my incorrect input!).

I would be very glad for an explanation on this situation. Maybe
something escaped my attention.

I can confirm that in all other cases (including very, very similar
cases), Maxima has been perfect in its replies with respect to 
Laplace transformations. Just the incorrect input led to an incorrect
output.

Many thanks and best regards,


Nikos