A first person narration is filtered through the narrator's perspective and told using the narrator's voice. As a result, first person is often moving swiftly between observation, thought, description of action, and more. All of this is coming from the narrator's consciousness. Let's take a closer look.
In Raymond Carver's short story “Cathedral," the narrator's wife has a friend from her past come to visit—a blind man name Robert. The narrator is uncomfortable with this. Late in the evening of his arrival, the wife goes upstairs to change, leaving the narrator and Robert alone:
After she'd left the room, he and I listened to the weather report and then to the sports roundup. By that time, she'd been gone so long I didn't know if she was going to come back. I thought she might have gone to bed. I wished she'd come back downstairs. I didn't want to be left alone with a blind man. I asked him if he wanted another drink, and he said sure.
This passage starts with a report of what happened—they listened to the weather and sports—then transitions into the narrator's thoughts about his wife's intentions and his wish that she come back. Then the passage moves back to the action, summarizing this time: “I asked him if he wanted another drink, and he said sure." There's no need to set his thoughts off with formatting or punctuation. They're a part of the natural unfolding of his experience of the moment.
There are certainly some instances where italicizing thought may make sense. In Tom Paine's short story “The Anarchist Convention," the narrative unfolds as if the youthful narrator is recounting the events to a friend:
Late that night there are these loons going by in the moonlight, just riding the raging Mississippi, and I think, that's me and my life, I'm one of those loons. It sounds corny and all, but at the time Bugeye and I were into it and we made loon calls until we passed out.
Here, the narrator's thoughts aren't simply unfolding. Instead, he's deliberately pointing out the thought, summing up what may have been a complex experience in straightforward, direct language. Compare that with this excerpt later in the story:
Then we seemed to wake up and we were in the Rockies. Man, those are some serious mountains. Like I'm beginning to get a sense of how big this country is, you know.
Again, we get the narrator's thoughts, but this time the narrator isn't pointing the thought out; he's simply having it. And that's often enough to indicate a thought.