Let $f ( x ) = \int _ { 0 } ^ { x } \frac { \sin t } { t ^ { 2 } + 1 } d t . \text { Find } f ^ { \prime } ( x )$

Let $f ( x ) = \int _ { 0 } ^ { x } \frac { \sin t } { t ^ { 2 } + 1 } d t . \text { Find } f ^ { \prime } ( x )$

A) $\frac { \sin t } { t ^ { 2 } + 1 }$

B) $- \frac { \sin t } { t ^ { 2 } + 1 }$
C) $\frac { \cos x } { x ^ { 2 } + 1 }$
D) $- \frac { \sin x } { x ^ { 2 } + 1 }$
E) $\frac { \sin x } { x ^ { 2 } + 1 }$

F) $- \frac { \cos x } { x ^ { 2 } + 1 }$

G) $\frac { \cos x } { 2 x }$

H) $- \frac { \cos x } { 2 x }$

Correct Answer:

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