JEE Main 2015 · 4 Apr · Shift 1, Mathematics question 75

$36-12x+x^2=(6-x)^2$. Under $x\to6-x$ (which maps [2, 4] to itself) the integrand $f$ becomes $1-f$. So $2I=\int_2^41\,dx=2$ and $I=1$.