The number of points where f(x) = [sinx + cosx] (where [.] denotes the greatest integer function), x ∈ (0, 2π) is not continuous is

5

f(x) will be discontinuous at those points, where sinx + cosx is an integer, which is the case for $x∈\begin{Bmatrix}\frac{π}{2},\frac{3π}{4},π,\frac{3π}{2},\frac{7π}{4}\end{Bmatrix}$.

Thus f(x) is discontinuous exactly for five values of x.

Hence (C) is correct answer.