Let \(f:[0, \infty) \rightarrow[0, \infty)\) be defined as \(f(x)=\int_0^x[y] d y\), where \([x]\) is the greatest integ…

\(f \) is differentiable at every point in \([0, \infty)\)

\(f\) is continuous everywhere except at the integer points in \([0, \infty)\).

\(f\) is continuous at every point in \([0, \infty)\) and differentiable except at the integer points.

\(f\) is both continuous and differentiable except at the integer points in \([0, \infty)\).