Verified answer

Let's integrate it and find out.

y' = sin^2(x) = (1/(2i) (e^(ix) - e^(-ix)))^2

= -1/4 (e^(2ix) + e^(-2ix) - 2)

This is easy to integrate.

y - C = -1/4 [(e^(2ix) + e^(-2ix))/(2i) - 2x]

= -1/4 (sin(2x) - 2x)

= x/2 - sin(2x)/4

This is indeed an elementary antiderivative, so (a) and (b) are true.

Not sure what the difference between an elementary anti-derivative and a normal anti-derivative is but an anti-derivative does exist for sin^2(x).