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Mathematics
Problem
Explain in one or two sentences why, if
f
f
f
is continuous at
x
=
c
x=c
x
=
c
, then
d
d
x
(
∫
a
x
f
(
t
)
d
t
)
∣
x
=
c
=
f
(
c
)
\dfrac{d}{dx}\left(\displaystyle\int_{a}^{x} f(t)\,dt\right)\bigg|_{x=c}=f(c)
d
x
d
(
∫
a
x
f
(
t
)
d
t
)
x
=
c
=
f
(
c
)
.
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