# Suppose f is such , that $f(-x) =-(x)$ for every real x and $\int\limits_0^1 f(x)x=5$ then $\int \limits _{-1}^0 =?$

$\begin {array} {1 1} (a)\;20 \\ (b)\;5 \\ (c)\;0 \\ (d)\;-5 \end {array}$

By using property
$\int \limits_{-0}^a f(x)=0$
$f(x) =-f(x) =>0$
$\int \limits _{-1} ^1 f(x) =0$
=>$\int \limits_{-1}^0 f(x) dx+ \int \limits_0^1 f(x) dx=0$
=>$\int \limits_{-1}^0 f(t) dt+5=0$
=>$\int \limits_{-1}^0 f(t) dt=-5$
Hence d is the correct answer