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How to enter an integral in a formula and have mathematica *not*

I have a certain integral, part of a larger expression, that can be
expressed in terms of incomplete gamma functions by Mathematica.  But
in carrying out the definite integral and forcing it to be written in
terms of gamma functions, this introduces branch points and other
unnecessary complications.  I want the integral left alone and
evaluated numerically, but I still want to express the general formula
for this large expression with the unevaluated integral in place.

For example, I'd like

f[x_] = (stuff) + int_{0}^{1} (g[s,x]) ds

where the definite integral is expressed in the usual Mathematica

What I do *not* want Mathematica to do at this stage is to do the
integral analytically and write it in terms of special functions.
Instead, I just want to later make a list of values for  f[x]  and
have the integral done numerically.

How can I program this?


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