Let $f(x)=\left[x^{2}-x\right]+|-x+[x]|$, where $x \in \mathbb{R}$ and $[t]$ denotes the greatest integer less than or equal to $t$. Then, $f$ is :

Question

continuous at $x=0$, but not continuous at $x=1$

continuous at $x=0$ and $x=1$

continuous at $x=1$, but not continuous at $x=0$

not continuous at $x=0$ and $x=1$

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