If $f$ is an even function then
Answer & explanation
Correct answer: option 2
$\int_{-a}^{a}f(x)dx=\int_{-a}^{0}f(x)dx+\int_{0}^{a}f(x)dx$. In $\int_{-a}^{0}f(x)dx$ substitute $x=-z$, then the integral becomes $\int_{0}^{a}f(z)dz$ since $f$ is an even function(i.e $f(x)=f(-x)$). So the sum is 2$\int_{0}^{a}f(x)dx$.