d
d
x
∫
a
x
f
(
t
)
d
t
=
\displaystyle {\frac{{{d}}}{{{\left.{d}{x}\right.}}}}{\int_{{a}}^{{x}}}{f{{\left({t}\right)}}}\ {\left.{d}{t}\right.}=
d
x
d
∫
a
x
f
(
t
)
d
t
=
f
(
t
)
\displaystyle {f{{\left({t}\right)}}}
f
(
t
)
f
(
x
)
−
f
(
a
)
\displaystyle {f{{\left({x}\right)}}}-{f{{\left({a}\right)}}}
f
(
x
)
−
f
(
a
)
F
(
x
)
−
F
(
a
)
\displaystyle {F}{\left({x}\right)}-{F}{\left({a}\right)}
F
(
x
)
−
F
(
a
)
, where
F
\displaystyle {F}
F
is any antiderivative of
f
\displaystyle {f}
f
.
f
(
a
)
\displaystyle {f{{\left({a}\right)}}}
f
(
a
)
f
(
x
)
\displaystyle {f{{\left({x}\right)}}}
f
(
x
)
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