\text { 1. Imitate the example in Video } 7.10 \text { to compute } \int_{0}^{2}\left[2 x+3 x^{2}-x^{3}\right] d x \text { using Riemann sums. Useful } formulas: \sum_{j=1}^{N} j=\frac{N(N+1)}{2}, \quad \sum_{j=1}^{N} j^{2}=\frac{N(N+1)(2 N+1)}{6}, \quad \sum_{j=1}^{N} j^{3}=\frac{N^{2}(N+1)^{2}}{4}