Integration - Improper Integrals and Convergence

Evaluate each definite integral.

1. \(\displaystyle\displaystyle\int_{-1}^{4} x^3 \ \mathrm{d}x\)
2. \(\displaystyle\displaystyle\int_{-\frac{1}{2}}^{\frac{1}{2}} (4 + 7x^2) \ \mathrm{d}x\)
3. \(\displaystyle\displaystyle\int_{2}^{5} \sqrt{y^3} \ \mathrm{d}y\)
4. \(\displaystyle\displaystyle\int_{-2}^{3} 2 + \frac{1}{\sqrt[3]{x}} \ \mathrm{d}x\)