Integral Problem (3)

$if \underset{1}{\overset{3}{\int }}2 f\left(x\right)dx=20 and\underset{5}{\overset{3}{\int }}f\left(x\right)dx=3 calculate \underset{1}{\overset{5}{\int }}f\left(x\right)dx$

$ans:$
$\underset{1}{\overset{3}{\int }}2 f\left(x\right)dx=20, so 2\underset{1}{\overset{3}{\int }} f\left(x\right)dx=20$
$\underset{1}{\overset{3}{\int }} f\left(x\right)dx=10$
$\underset{5}{\overset{3}{\int }}f\left(x\right)dx=3, so \underset{3}{\overset{5}{\int }}f\left(x\right)dx=-3$
$\underset{1}{\overset{5}{\int }}f\left(x\right)dx =\underset{3}{\overset{5}{\int }}f\left(x\right)dx + \underset{1}{\overset{3}{\int }} f\left(x\right)dx$
$\underset{1}{\overset{5}{\int }}f\left(x\right)dx = -3+10$
$\underset{1}{\overset{5}{\int }}f\left(x\right)dx = 7$