im doing my DE HW and i dont understand how the book came out with an answer.. This is separable variables with an initial value.

(dx/dt) = 4(x^2+1) the intial value is: x((pi)/4)=1

the answer is: y= sin ((1/2)x^2+c)

and i have no idea where the sin came from...i know im probaly missing a rule somewhere, thanks for any help to get the jucices going!