If $\int_{-1}^4f(x) dx = 4$ and $\int_2^4(3-f(x)) dx = 7$, the value of $\int_2^{-1}f(x)dx$ is
Answer & explanation
Correct answer: option 3
$∵\int_{-1}^4f(x) dx = 4$ and $\int_2^4(3-f(x)) dx = 7$
or $\int_4^{-1}f(x)dx=-4$ and $6-\int_2^4f(x)dx=7$
$∴\int_4^{-1}f(x)dx=-4,\int_2^4f(x)dx=-1$
$\int_2^{-1}f(x)dx=\int_2^4f(x)dx+\int_4^{-1}f(x)dx=-1-4=-5$