Let $f(x)=\frac{ba^{b}}{x^{b+1}}$ be the given function of pareto Pareto distribution with parameters $a$ and $b$; where: $a<x<\infty$ and $a>0$ $b>0$. Show that $f$ is pdf.
My Working:
$\int_{a}^{\infty} \frac{ba^{b}}{x^{b+1}} dx=-ba^b[\frac{x^{-b}}{b}]|_a^\infty=-a^{b}[a^{-b}-\infty^{-b}]=-a^{b-b}=-1$
Where I am making a mistake. The result should be $1$ in order for $f$ to be the pdf.