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If f(x) = A sin (πx ) + B, f' (1/2)=√2 and ∫f(x)dx ,x∈ (0,1) =2A/π ,Then which of the following is/are correct?

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If f(x) = A sin (πx ) + B, f' (1/2)=√2 and ∫f(x)dx ,x∈ (0,1) =2A/π ,Then which of the following is/are correct? 

(A) constant B is zero & A can be any real number

(B) A + B = 4/π

 (C) A + B = 4/π+ 2

 (D) A – B = 4/π

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Correct Option :- (B) (D)

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