The range of function y = sin * absolute value x + SiNx

The range of function y = sin * absolute value x + SiNx

y=sin|x|+sinx
x∈[2kπ ,(2k+1)π],y=2sinx,y∈[0,2]
x∈[(2k-1)π ,2kπ],y=0
The range of Y is [0,2]