最大值y=2*1+3=5最小值y=2*（-1）+3=1
令2kπ-π/2≤x-π/3≤2kπ+π/2得2kπ-π/6≤x≤2kπ+5π/6,k为整数
令2kπ+π/2≤x-π/3≤2kπ+3π/2得2kπ+5π/6≤x≤2kπ+11π/6,k为整数
所以,函数y=2sin(x-π/3)+3 的值域为[1,5]
单调增区间为[2kπ-π/6,2kπ+5π/6],k为整数；
单调减区间为[2kπ+5π/6,2kπ+11π/6],k为整数