Integrating Squares

Calculus Level 2

Knowing that $\sin^2 x + \cos^2 x = 1$ , then which of the following is true?

(A): $\displaystyle \int_0^{\pi /2} \sin^2 x \, dx + \int_0^{\pi /2} \cos^2 x \, dx = \dfrac\pi2$ .
(B): $\displaystyle \int_0^{\pi /2} \sin^2 x \, dx = \dfrac\pi4$ .
(C): $\displaystyle \int_0^{\pi /2} \cos^2 x \, dx = \dfrac\pi4$ .