'definitely intrigued' is correct and usable in written English.
You can use it when you want to express that you have a strong interest in something. Example sentence: I'm definitely intrigued to learn more about this subject.
"They're definitely intrigued".
And, while I was definitely intrigued, a tiny voice inside my head kept repeating, "Don't lend him money".
"I was definitely intrigued," she said, "but I was a year younger and wasn't sure he was interested in me".
I wasn't convinced at first, but was definitely intrigued by the Spanish combination of morcilla, beans and mint.
Mr. Smokler, in turn, said he was "definitely intrigued by her, but our paths never crossed long enough".
William said how about we all get together for bridge, and I said I much preferred swimming and he looked definitely intrigued.
From what I've heard, Netflix is something that definitely intrigues Apple.
Aside from the steep requirement of apparent (temporary?) platform lock-in, I'm definitely much more intrigued by the Gear, but I also suspect both devices will find a mostly limited receptive audience among consumers.
Although this is no Reconstructing Amelia, it definitely kept me intrigued.
Also seeing improvement was Jane Boursaw of AOL's TV Squad, commenting "Tonight's episode definitely got me intrigued about fringe science, and this is the first time I can really say I'm looking forward to the next episode.
Naturally, I was utterly intrigued, but, definitely "Yeah, sure!" skeptical about the whole thing... although this girl and her friends all seemed sane and even kinda cool looking, actually.
