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Mathematics
Problem
Let
f
f
f
be integrable on
[
a
,
c
]
[a,c]
[
a
,
c
]
, and let
b
b
b
satisfy
a
<
b
<
c
a<b<c
a
<
b
<
c
. Which of the following is always equal to
∫
a
c
f
(
x
)
d
x
\displaystyle\int_{a}^{c} f(x)\,dx
∫
a
c
f
(
x
)
d
x
? a)
∫
a
b
f
(
x
)
d
x
+
∫
c
b
f
(
x
)
d
x
\displaystyle \int_{a}^{b} f(x)\,dx + \int_{c}^{b} f(x)\,dx
∫
a
b
f
(
x
)
d
x
+
∫
c
b
f
(
x
)
d
x
b)
∫
a
b
f
(
x
)
d
x
+
∫
b
c
f
(
x
)
d
x
\displaystyle \int_{a}^{b} f(x)\,dx + \int_{b}^{c} f(x)\,dx
∫
a
b
f
(
x
)
d
x
+
∫
b
c
f
(
x
)
d
x
c)
∫
a
b
f
(
x
)
d
x
−
∫
b
c
f
(
x
)
d
x
\displaystyle \int_{a}^{b} f(x)\,dx - \int_{b}^{c} f(x)\,dx
∫
a
b
f
(
x
)
d
x
−
∫
b
c
f
(
x
)
d
x
d)
∫
a
c
∣
f
(
x
)
∣
d
x
\displaystyle \int_{a}^{c} \lvert f(x)\rvert \,dx
∫
a
c
∣
f
(
x
)∣
d
x
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