can someone help me with calculus please?? thank u so much?

Question

find all extrema in the interval [0,2π] if y = x + sin x

Answer 1

the extrema exist at values of x where dy/dx = 0
y = x + sin x
if
0 = dy/dx = 1 + cosx
then
cosx = -1
gives
x = π
as the only solution on [0,2π]

,.,.,

Answer 2

y´= 1+cosx = 0 cos x=-1 and x=pi but the sign of y´is always >=0
so at x= pi there is no extreme
The absolute minimum is 0 at x=0 and the absolute maximum is
2pi at x=2pi