The image contains mathematical problems, so let me process and extract the text for solving these problems. Hold on.Here are the mathematical problems extracted from the image:

1. Consider the function:

   \begin{cases} 5 + x, & \text{if } 0 < x \\ 5 - x, & \text{if } 0 \geq x \end{cases}$$ Use $$f(x)$$ to evaluate: $$\int_{-10}^{7} f(x) \, dx$$

2. Use the anti-derivative method to find the area under the graph of: $y = x^3 - 1$ over the interval $[0,2]$.

3. Integrate: (a) $\int \sec^2(3x) \, dx$

   (b) $\int x \sin\left(\frac{x}{2} + x\right) \, dx$

Would you like me to solve these problems step by step?