Hello, and welcome to TMH!

Let's begin by writing what we're given:

\(\displaystyle \int_{-3}^5 f(x)\,dx=12\)

Now, we may break up the LHS as follows:

\(\displaystyle \int_{-3}^3 f(x)\,dx+\int_{3}^5 f(x)\,dx=12\)

Since we are given that \(f(x)\) is an odd function, we know:

\(\displaystyle \int_{-3}^3 f(x)\,dx=0\)

And so we are left with:

\(\displaystyle \int_{3}^5 f(x)\,dx=12\)

Does that make sense?