About this passageSze-ma Niu was a disciple, and the Analects record him elsewhere as an anxious man; the chapter immediately following has him grieving that other men have brothers and he has none. He asks what the junzi — Legge's "superior man", meaning a person who has become reliable rather than one of high birth — is like, and gets an answer he does not accept, so he presses. The second answer relocates the question: it does not say anxiety is unwarranted, it says where to look to find out whether it is.
Sze-ma Niu asked about the superior man. The Master said, "The superior man has neither anxiety nor fear."
"Being without anxiety or fear!" said Niu;—"does this constitute what we call the superior man?"
The Master said, "When internal examination discovers nothing wrong, what is there to be anxious about, what is there to fear?"
In plainer words
Sze-ma Niu asked what a person of real character is like. Confucius said: they are neither anxious nor afraid. "That's all?" said Niu. Confucius said: look inside honestly, and if you find nothing wrong there, what is left to be anxious about? What is left to fear?
A restatement in modern English, written for this collection. The passage above is the text; this is one way of putting it.