Why is the definite integral of the nth power of X on (0,1) 1 / N + 1?

Why is the definite integral of the nth power of X on (0,1) 1 / N + 1?

The definite integral of the nth power of X on (0,1) = the difference after 1 / (n + 1) * x ^ (n + 1) is substituted into 1 and 0,
That is 1 / (n + 1) * 1 ^ (n + 1) - 1 / (n + 1) * 0 ^ (n + 1) = 1 / (n + 1)