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"Does this subject belong in a science class though? I am not that familiar with the topic but I heard it is based in Creationism. If that is true, then it belongs in religious type classes."

It has nothing to do with theology. It is mostly mathematics-based. Intelligent Design simply says, "there are certain marks that indicate that an object or system is the result of an intelligent designer". This includes humans or other creatures that are intelligent designers. To put the method shortly, Intelligent Design looks for systems that are organized within a chaotic system. Dembski has written extensively about the mathematics behind this in his books. I've written a short explanation of the idea here:

http://crevo.blogspot.com/2005/03/setting-facts-straight-on-intelligent.html

There is also another aspect of Intelligent Design which is focused on removing certain assumptions from science, namely materialism. Materialism is a rather bad philosophy anyway, for numerous reasons.

"Materialism", or material explanations of phenomenon, cannot be removed from Science. If it is immaterial it cannot be measured, observed or predicted. Without observation, measurement or prediction there is no Science.

So I have two questions for you...

1) How successful have non-material explanations been in observing and predicting the universe; as well as settling issues of factual disagreement?

2) How many Scientific theories are dependent upon an unobservable and unmeasurable force acting upon matter with an unknown mechanism?

This is a measure of the highest amount of improbability available in the universe. According to Dembski, events over this bound are improbable no matter how many probabilistic resources you apply to them. He calculates by estimating the number of particles in the universe, combining it with available time, and the fastest rate that matter can change states (corresponding to Planck time, again, another item outside my field).

This is a quote from your web link. This argument is totally bogus, false, and logically invalid (and the heart of his case). What Dumbski is saying is that he is so all-knowing about what is "probable" and what isn't that what he has decided cannot be probable cannot be probable. Period. What a circular argument! (second only to an Intelligent Designer being the only valid explanation for that which the ID advocate cannot understand took place in any other fashion - therefore there must be an Intelligent Designer - [as opposed to an Unintelligent Designer?]).

Notice that what he is really saying is that whatever "events" he claims are so improbable that they could not have taken place is just a dishonest way of saying they are impossible. He knows that if he said this outright he would be utterly rejected. It is either it is improbable to the point of impossibility, or it is possible.

Thus he is merely playing a word game to disguise what he is saying rather than stating what he is saying outright, thus revealing he knows what he is saying is not science. The fact that such events in question are so highly improbable they could not have taken place is refuted by the fact that they have already taken place.

This isn't evidence of Intelligent Design, it is evidence of dishonest argumentation to somehow get Creationism to be considered science under the rubric of ID.