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): \(\displaystyle \int_0^{\pi /2} \cos^2 x \, dx = \dfrac\pi4\).