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Mathematics
Problem
Let
g
(
x
)
=
∫
2
x
f
(
t
)
d
t
g(x)=\int_{2}^{x} f(t)\,dt
g
(
x
)
=
∫
2
x
f
(
t
)
d
t
for a continuous function
f
f
f
. Which of the following expressions is equal to
g
(
8
)
−
g
(
5
)
g(8)-g(5)
g
(
8
)
−
g
(
5
)
? a)
∫
2
8
f
(
t
)
d
t
\displaystyle \int_{2}^{8} f(t)\,dt
∫
2
8
f
(
t
)
d
t
b)
∫
5
8
f
(
t
)
d
t
\displaystyle \int_{5}^{8} f(t)\,dt
∫
5
8
f
(
t
)
d
t
c)
∫
2
5
f
(
t
)
d
t
\displaystyle \int_{2}^{5} f(t)\,dt
∫
2
5
f
(
t
)
d
t
d)
∫
8
5
f
(
t
)
d
t
\displaystyle \int_{8}^{5} f(t)\,dt
∫
8
5
f
(
t
)
d
t
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