A function $f$ is positive on $\left[0,1\right]$ with ${\int }_0^{1}f(x)dx=4$ and negative on $\left[1,3\right]$ with ${\int }_1^{3}f(x)dx=-1$. What is the total AREA between the graph and the x-axis on $\left[0,3\right]$?

Evaluate ${\int }_4^{8}2dx$.

Given ${\int }_0^{3}f(x)dx=6$, ${\int }_3^{8}f(x)dx=-6$ and ${\int }_0^{8}g(x)dx=-4$, find ${\int }_8^0\left(f(x)+g(x)\right)dx$.

Given ${\int }_4^{5}f(x)dx=-6$, find ${\int }_5^{4}f(x)dx$.

Given ${\int }_1^{6}f(x)dx=3$ and ${\int }_1^{6}h(x)dx=7$, find ${\int }_1^6\left(5f(x)-5h(x)\right)dx$.

A function $f$ is positive on $\left[0,3\right]$ with ${\int }_0^{3}f(x)dx=8$ and negative on $\left[3,5\right]$ with ${\int }_3^{5}f(x)dx=-7$. What is the total AREA between the graph and the x-axis on $\left[0,5\right]$?

Given ${\int }_0^{4}h(x)dx=8$ and ${\int }_0^{7}h(x)dx=7$, find ${\int }_4^{7}h(x)dx$.

Given ${\int }_4^{7}f(x)dx=6$, find ${\int }_7^{4}f(x)dx$.

Evaluate ${\int }_0^{3}2dx$.

Given ${\int }_1^{6}f(x)dx=-2$ and ${\int }_1^{6}h(x)dx=8$, find ${\int }_1^6\left(3f(x)-5h(x)\right)dx$.

Given ${\int }_0^{3}f(x)dx=7$, ${\int }_3^{8}f(x)dx=-9$ and ${\int }_0^{8}g(x)dx=-6$, find ${\int }_8^0\left(f(x)+g(x)\right)dx$.

Given ${\int }_0^{2}f(x)dx=5$, find ${\int }_2^{0}f(x)dx$.

Given ${\int }_0^{3}f(x)dx=-2$, ${\int }_3^{8}f(x)dx=7$ and ${\int }_0^{8}g(x)dx=2$, find ${\int }_8^0\left(f(x)+g(x)\right)dx$.

Evaluate ${\int }_1^{2}9dx$.

Given ${\int }_0^{4}h(x)dx=-8$ and ${\int }_0^{7}h(x)dx=-5$, find ${\int }_4^{7}h(x)dx$.

Given ${\int }_0^{3}f(x)dx=-5$, ${\int }_3^{8}f(x)dx=2$ and ${\int }_0^{8}g(x)dx=-9$, find ${\int }_8^0\left(f(x)+g(x)\right)dx$.

Given ${\int }_1^{6}f(x)dx=-2$ and ${\int }_1^{6}h(x)dx=1$, find ${\int }_1^6\left(4f(x)-3h(x)\right)dx$.

Given ${\int }_0^{5}p(x)dx=3$ and ${\int }_0^{8}p(x)dx=-2$, find ${\int }_5^{8}p(x)dx$.

Given ${\int }_2^{6}f(x)dx=-8$, find ${\int }_6^{2}f(x)dx$.

Given ${\int }_1^{6}f(x)dx=2$ and ${\int }_1^{6}h(x)dx=-4$, find ${\int }_1^6\left(3f(x)-4h(x)\right)dx$.

Given ${\int }_0^{3}g(x)dx=8$ and ${\int }_0^{6}g(x)dx=-9$, find ${\int }_3^{6}g(x)dx$.

Evaluate ${\int }_4^{10}-3dx$.

Given ${\int }_1^{6}f(x)dx=-3$ and ${\int }_1^{6}h(x)dx=4$, find ${\int }_1^6\left(2f(x)-5h(x)\right)dx$.

Given ${\int }_1^{6}f(x)dx=8$ and ${\int }_1^{6}h(x)dx=-2$, find ${\int }_1^6\left(5f(x)-5h(x)\right)dx$.

Given ${\int }_0^{2}f(x)dx=8$ and ${\int }_0^{5}f(x)dx=5$, find ${\int }_2^{5}f(x)dx$.

Given ${\int }_2^{6}g(x)dx=-9$, find ${\int }_6^{2}g(x)dx$.

A function $f$ is positive on $\left[0,2\right]$ with ${\int }_0^{2}f(x)dx=9$ and negative on $\left[2,4\right]$ with ${\int }_2^{4}f(x)dx=-1$. What is the total AREA between the graph and the x-axis on $\left[0,4\right]$?

Given ${\int }_0^{4}r(x)dx=-5$ and ${\int }_0^{7}r(x)dx=7$, find ${\int }_4^{7}r(x)dx$.

Given ${\int }_0^{4}g(x)dx=2$ and ${\int }_0^{7}g(x)dx=-5$, find ${\int }_4^{7}g(x)dx$.

Given ${\int }_0^{3}f(x)dx=-9$, ${\int }_3^{8}f(x)dx=-4$ and ${\int }_0^{8}g(x)dx=-8$, find ${\int }_8^0\left(f(x)+g(x)\right)dx$.