Let be a continuous function given by for all

MATHEMATICS · Single correct

Problem

Let

f:\mathbb{R}\to\mathbb{R}

be a continuous function given by

f(x+y)=f(x)+f(y)

for all

x,y\in\mathbb{R}

. If

\int_0^2f(x)\,dx=\alpha

, then

\int_{-2}^2f(x)\,dx

is equal to (1)

2\alpha

(2)

\alpha

(3)

0

(4) None of these