Vocabulary - Interval

An interval $[i,j]$ is a contiguous subarray from index i to index j, inclusive. The length is j. I + $1$. In interval DP, you typically iterate by length.

First solve all intervals of length $1$(base cases), then length $2$, then length $3$, up to the full array. The answer you want is usually $dp[0][n-1]$ or $dp[1][n]$, depending on whether you use $0$-indexed or $1$-indexed arrays.