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Antidifferentiation: Finding $f(\theta )$

APCALC-7MZSNB

If $f^{ \prime \prime }\left( \theta \right) =\sin { \theta }$, $f^{ \prime }\left( \cfrac { \pi }{ 2 } \right) =0$, and $f\left( \cfrac { \pi }{ 2 } \right) =1$, what is $f(\theta )$ ?

A

$-\cos { \theta }$

B

$-\cos { \theta } +1$

C

$-\sin { \theta }$

D

$-\sin { \theta } +2$