f(x)=向量OA×向量OB+m
=2sin^2x-2√3sinxcosx+1+m
=1-cos2x-√3sin2x+1+m
=-2sin(2x+π/6)+2+m
1.单增区间为2x+π/6∈[2kπ+π/2,2kπ+3π/2]
x∈[kπ+π/6,kπ+2π/3]
2.当x∈[π/2,π] 2x+π/6∈[7π/6,13π/6]
f(x)max=2+m+2=m+4 f(x)min=2*(-1/2)+2+m=m+1
所以m+4=5 m+1=2
解得m=1