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g:[0,pi]toR is defined as g(x)={("max"{"...

`g:[0,pi]toR` is defined as `g(x)={("max"{"sin"x,1/2},"where",x epsilon[0,(pi)/2]),("min"{"sin"x,1/2},"where",x epsilon((pi)/2,pi]):}`
then answer following question
`lim_(to(pi^(-))/2)g(x)-lim_(xto(pi^(+))/2)g(x)` is equal to

A

`1`

B

`-1`

C

`1/2`

D

`-1/2`

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