Fine the maximum and minimum value of $f(x) = x + \sin 2x$ in the invervat $0, 2\pi$

Question

$(A)\; 2\pi, 0$
$(B)\; \pi , 0$
$(C)\; \frac{2 \pi}{3}, 0$
$(D)\; \frac{4 \pi}{3} , 0$