"According to one of many sources, the definition of intention is described as 'Right intention [...]"
Notice that the source you link to is not defining "intention" (aka "volition" from pali cetanā, or the related "volitional formations", "kamma formations" or "formations" from pali saṅkhāra), the psychological aspect of the mind associated to kamma, but "Right Intention" (also translated as "right thought", "right aspiration", "right resolve" from pali sammā sankappa) which describes instructions to develop oneself in the path, not an element of the psychological framework.
"If my thought is the result of anger however i do not have intent to harm is that not the result of rational thought?"
Just to contextualize:
[The Buddha:] "What do you think, Rahula: What is a mirror for?"
[Rahula:] "For reflection, sir."
[The Buddha:] "In the same way, Rahula, bodily acts, verbal acts, and mental acts are to be done with repeated reflection.
"Whenever you want to perform a bodily act, you should reflect on it: 'This bodily act I want to perform — would it lead to self-affliction, to the affliction of others, or to both? Is it an unskillful bodily act, with painful consequences, painful results?' [...]
"If, on reflection, you know that it is leading to self-affliction, to affliction of others, or both... you should give it up. But if on reflection you know that it is not... you may continue with it."
-- MN 61
If we understand a thought as an (volitional) act of angry thinking with intention to harm, and upon seeing the danger in such thinking, one abandons the intention to harm, you could call this reflection a "rational thought". Afterwards, while still angry, if one has another thought, a non-harming thought, this is another act of thinking with another intention behind it.
I guess you could say this second intention is the "result of a rational thought", but only to the extent you're explaning that this previous reflection influenced it.
But to the extent that "result" means a much closer relationship, I think it would risk hiding important details:
"Intention [cetanā], I tell you, is kamma.
Intending, one does kamma by way of body, speech, & intellect.
"And what is the cause by which kamma comes into play? Contact is the cause by which kamma comes into play.
-- AN 6.63
"And what, bhikkhus, is dependent origination? With ignorance as condition, volitional formations [saṅkhārā] come to be; [...]
-- SN 12.2
"If i do act irrationally, to save or protect a life, is that not intention without thought?"
If one acts "irrationally to save a life", I'd say he is acting conscious and deliberately, not irrationally: that's his intention after all, "to save" (*). If he saves "by accident", then I'd say it was an unreflected, unaware act (with regards to that specific outcome, at least), with no intention to save, but with intention to, say, obtain something else (which, by accident, resulted in saving).
From my understanding of Theravada point of view, (and grossly speaking) intention is always behind an (bodily, verbal, mental) act. Intentions, however, are subject to be reshaped by one's own will.
Finally, intentions may be succeeded by careful reflection, or not. They may be shaped by previous introspection, just by deep habits, etc. or any combination of it.
(*) He may be "irrational" in his method, not in absense of intention or thought.