"I feel bad, as you can notice."
Translation:Je me sens mal, comme vous pouvez le constater.
Mal is an adverb literally meaning 'badly', mauvais is an adjective. I think mal is used quite often in phrases that dont french that do not translate well literally to english. E.g. J'ai mal à la tête, literally I am having badly in the head, actually makes more sense in english as 'I have pain in the head', 'my head hurts', or 'I have a headache'.
In "J'ai mal à la tête", "mal" is still a noun, even though the article is missing, which is not too unusual in expressions. The literal translation would be something like "I have badness in the head" - which could mean a lot of things, but is conventionally used to refer to a headache.