JEE Main 2021 Mathematics question

Let be defined as where [x] is the greatest integer less than or equal to x. Which of the following is true?

• (A)f is continuous at every point in and differentiable except at the integer points.Correct
• (B)f is both continuous and differentiable except at the integer points in .
• (C)f is continuous everywhere except at the integer points.
• (D)f is differentiable at every point in