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Mathematics
Problem
For real numbers
a
<
b
<
c
a<b<c
a
<
b
<
c
and an integrable function
g
g
g
, which of the following identities holds for all such
g
g
g
? a)
∫
a
b
g
(
x
)
d
x
=
∫
b
a
g
(
x
)
d
x
\displaystyle \int_{a}^{b} g(x)\,dx = \int_{b}^{a} g(x)\,dx
∫
a
b
g
(
x
)
d
x
=
∫
b
a
g
(
x
)
d
x
b)
∫
a
c
g
(
x
)
d
x
=
−
∫
c
a
g
(
x
)
d
x
\displaystyle \int_{a}^{c} g(x)\,dx = -\int_{c}^{a} g(x)\,dx
∫
a
c
g
(
x
)
d
x
=
−
∫
c
a
g
(
x
)
d
x
c)
∫
a
b
g
(
x
)
d
x
+
∫
b
c
g
(
x
)
d
x
=
−
∫
a
c
g
(
x
)
d
x
\displaystyle \int_{a}^{b} g(x)\,dx + \int_{b}^{c} g(x)\,dx = -\int_{a}^{c} g(x)\,dx
∫
a
b
g
(
x
)
d
x
+
∫
b
c
g
(
x
)
d
x
=
−
∫
a
c
g
(
x
)
d
x
d)
∫
a
c
g
(
x
)
d
x
=
∫
a
b
g
(
x
)
d
x
+
∫
c
b
g
(
x
)
d
x
\displaystyle \int_{a}^{c} g(x)\,dx = \int_{a}^{b} g(x)\,dx + \int_{c}^{b} g(x)\,dx
∫
a
c
g
(
x
)
d
x
=
∫
a
b
g
(
x
)
d
x
+
∫
c
b
g
(
x
)
d
x
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