Definite Integration question bank (Maths)

Let $f: \mathbf{R} \rightarrow(0, \infty)$ be a continuous decreasing function. Suppose $f(0), f(1), \ldots, f(10)$ are in a geometric progression with common ratio $\frac{1}{5}$. In which of the following intervals does the value of $\int_0^{10} f(x) d x$ lie?

If $p(t)=\frac{t(t-1) \cdots(t-2019)}{2019!}$, then the value of
$\int_0^1\left(\frac{1}{t+1}+\frac{1}{t+2}+\cdots+\frac{1}{t+2020}\right) p(-t-1) d t$ is: