I came across this problem which says:
Let $f:[-1,1]\rightarrow \ \mathbb{R}$ be continuous. Assume that $\int_{-1}^{1}f(t)\, dt =2$. Then $\lim_{n\to\infty} \int_{-1}^{1}f(t)\sin^2(nt)\,dt$ equals to
a) $0$
b) $1$
c) $f(1) - f(-1)$
d) Does not exist
I have taken $f(t)=1$ so that it satisfies the given definite integral. Then I see the solution to be $1$. Am I correct? I am looking for a better way to solve it. Please help.