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Mathematics
Problem
Give a brief reason why the function
F
(
x
)
=
∫
a
x
f
(
t
)
d
t
F(x)=\int_a^x f(t)\,dt
F
(
x
)
=
∫
a
x
f
(
t
)
d
t
is increasing at those points of
x
x
x
where
f
(
x
)
>
0
f(x)>0
f
(
x
)
>
0
and decreasing where
f
(
x
)
<
0
f(x)<0
f
(
x
)
<
0
, assuming
f
f
f
is continuous.
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