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Let F(x)=int(0)^(x)(cost)/((1+t^(2)))dt,...

Let `F(x)=int_(0)^(x)(cost)/((1+t^(2)))dt,0lex le2pi`. Then -

A

F is increasing in `((pi)/(2),(3pi)/(2))` and decreasing in `(0,(pi)/(2))` and `((3pi)/(2),2pi)`

B

F is increasing in `(0,pi)` and decreasing in `(pi,2pi)`

C

F is increasing in `(pi,2pi)` and decreasing in `(0,pi)`

D

F is increasing in `(0,(pi)/(2))` and `((3pi)/(2),2pi)` and decreasing in `((pi)/(2),(3pi)/(2))`

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