Suppose that a function f(x) defined in −1<x<1 satisfies the following properties (i) , (ii), (iii).(i) f′(x) is continuous.(ii) When −1<x<0, f′(x)<0, f′(0)=0, when 0<x<1, f′(x)>0.(iii) f(0)=−1Let F(x)=∫0x1+{f′(t)}2dt (−1<x<1). If F(sinθ)=cθ (c:constant) holds for −2π<θ<2π, then find f(x).1975 Waseda University entrance exam/Science and Technology calculusintegrationfunctiontrigonometryderivativecalculus computations