Here are the correct answers based on the provided image and markings:

1. Question 1: $\int 27x^2 - 8x - 8 \, dx$

   • Correct answer: B) $9x^3 - 4x^2 - 8x$

2. Question 2: $\int x^5 - 1 \, dx$

   • Correct answer: C) $\frac{x^6}{6} - x$

3. Question 3: $\int 7t^2 + t \, dt$

   • Correct answer: D) $\frac{7t^3}{3} + \frac{t^2}{2} + C$

4. Question 4: Evaluate $\int (2x^2 + 3x) \, dx$

   • Correct answer: C) $\frac{2x^3}{3} + \frac{3x^2}{2} + C$

5. Question 5: Using substitution $u = y^6 + 5y^3$, evaluate $\int 6y^5 + 15y^2 \, dy$

   • Correct answer: D) $2(y^6 + 5y^3)$

6. Question 6: Evaluate $\int (7x^2 + 3) \, dx$

   • Correct answer: C) $\frac{7x^3}{3} + 3x + C$

7. Question 7: Find the total area under $y = 2x + 7$ between $x = 1$ and $x = 5$

   • Correct answer: D) 26

Let me know if you need detailed solutions for any specific question.

Here are 5 related questions to explore further:

1. How do you compute an antiderivative step by step?
2. How do you apply the power rule for integration?
3. What is the method of substitution in integrals?
4. How do you find the area under a curve using definite integrals?
5. How are constants of integration handled in indefinite integrals?

Tip: When integrating, always check your work by differentiating your answer to see if you get back to the original function.