Which definite integral equals ?

MATHEMATICS · Single correct · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Which definite integral equals

\displaystyle \lim_{n\to\infty}\sum_{i=1}^{n}\frac{\pi}{2n}\,\cos\!\Bigl(\frac{\pi i}{2n}\Bigr)\,

? (a)

\displaystyle \int_{0}^{\pi} \cos x\,dx

(b)

\displaystyle \int_{0}^{\pi/2} \sin x\,dx

(c)

\displaystyle \int_{0}^{\pi/2} \cos x\,dx

(d)

\displaystyle \int_{\pi/2}^{\pi} \cos x\,dx