I think I have discovered an interesting result as an independent researcher in mathematics, can I use this to gain admission to a PhD program? I am an independent math researcher and I think I have discovered an interesting result in a particular field (in math). I would like to present my result in front of a committee of PhD admission.

My question:  Is there a possibility that i can prove my research skills and the result in such a way that some committee will decide to integrate me into its doctoral (or graduate ) program ?

N.B. Do I need to publish the result (Do you think that all maths journals and referees can be absolutely trusted?) in order that it will appear credible, or at least to capture the attention of the members or any one who can recommend me to a PhD or graduate school?
There are some problematical implicit assumptions in the question. First, PhD admission committees do not conduct interviews of the sort you imagine. They might look at a manuscript accompanying an application, but there's much more substance to an application for graduate-program admission than showing one item. (For that matter, professional mathematicians' perception of your work may be different than your own, so it might be unwise to put so much stock in the anticipated saving grace of your research work.)

You'll want letters of recommendation attesting to your future potential, based on your current and past performance, whether in literal math classes or in informal situations. If you've done a nice piece of work, this would contribute a bit, but it's by no means enough on its own.

Although it's of dubious serious value, the GRE Math Subject Test is something you'd want to sign up for and take it the Autumn before applying to grad schools (which needs to be done by early December for entrance the following Fall). 

Publication is nice, but is an enterprise in itself, and not strictly necessary. For one thing, conventional peer-reviewed publication takes about a year or more in the best of times, so it wouldn't help you in the immediate future.

As in @PerAlexandersson's answer, you'd definitely want to type up your work in LaTeX or TeX, and make it conform to the general style of papers you can see, for example, on http://arxiv.org/archive/math  There is nothing truly sacred about the formatting and such, but for someone trying to enter, it is often best to be generally conforming in superficial regards, to avoid too loudly announcing that you're an outsider.

Not all "publishers" are serious or honest, no. One way to form a list of plausible submission venues is to look at papers on arXiv, submitted by people with .edu emails, and see what journals their bibliographic entries have appeared in. Some of these will be very-high-status, so possibly inappropriate, but if you sift through you will have a good inclusive list of the most legitimate journals. Still, no compulsion to try to publish in this sense before applying to grad school. If anything, it'd be more important to simply have your result typed up in LaTeX and to create a fairly conformist appearance (for example, matching the arXiv papers). You can even get TeX templates from those papers, to see how the effects are achieved, since the TeX source is available at arXiv.

The traditional journals' editors and referees can generally be trusted, because they have much to lose by bad behavior. Still, there are no guarantees, so pre-publication [sic] on arXiv would establish your priority. 

But, in any case, there are more parts to grad school application than just one or two or... pieces of work. Most math depts' graduate programs have web pages that elaborate on what documentation is required.