-π/2 ≤ x ≤ π/2
-π/2 +π/3 ≤ x +π/3 ≤ π/2 + π/3
-π/6 ≤ x +π/3 ≤ 5π/6
-1/2 ≤ sin(x +π/3) ≤ 1
-1 ≤ 2sin(x +π/3) ≤ 2
-1 ≤ f(x) ≤ 2
所以
最大值是 2
最小值是 -1