The correct option is D [0, (b - a )]
Whenever we are asked to find the interval in which an integral is lying we have to see the interval in which the integrand is lying.
Here, we have sin2x as integrand. We know that sin2x lies in the interval [0,1].
So, 0≤sin2x≤1
Also we know if a function f(x) lies between [m , M]
I.e. if m≤f(x)≤M
Then (b−a) m≤∫baf(x) dx ≤(b−a)M
So, using this we can say that -
(b−a).0≤∫basin2(x)dx≤(b−a).1=0≤∫basin2(x)dx≤(b−a)
So, ∫basin2(x)dx will lie in the interval [0, (b - a )