Let $f:[0,\infty ) \to [0,\infty )$ be defined as $f(x) = \int_0^x {[y]dy}$

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

1. A f is continuous at every point in $[0,\infty )$ and differentiable except at the integer points. Correct answer
2. B f is both continuous and differentiable except at the integer points in $[0,\infty )$.
3. C f is continuous everywhere except at the integer points in $[0,\infty )$.
4. D f is differentiable at every point in $[0,\infty )$.