Consider y = x^2 and f(x) where f(x) , is a differentiable function satisfying f(x+1) + f(z-1) = f(x+z) ; x,z R and f(0) = 0 ; f'(0) = 4 . If area bounded by curve y = x^2 and y = f(x) is , find the value of ( 3 16 ) .