for what value of p does the integral converge

Question

For what value of p does $\int_0 ^1 x^p dx$ converge?

So I used improper integral value for this, looking at the result

$$\lim_{p\to 0+} {1\over p+1}(x^{p+1}-p^{p+1})$$

*** I made a mistake, I got it now

$p\gt -1$