Hello I'm in AP calculus AB and I'm having problems understanding these 10 questions regarding anti derivatives and definite integrals. If you could please help me understand how to do these problems step by step up for my comprehension , I would gladly appreciate it. Thank you for all that you do.

Find the particular solution that satisfies the differential equation and the initial condition. 8. f' (x) = 4x2, f(-1) = 3 9. f"(x) = sin x , f'(0) = 1, f (0) = 6 10. A particle moves along the x-axis at a velocity of v(t) = t > 0. At time t = 1, its position is x = 4. a. Find the acceleration function for the particle. b. Find the position function for the particle.Name: Date: In Class Assignment: Antiderivatives and Indefinite Integration Find the indefinite integral. 1. S(x5 + 1) dx 2. S(8+3 - 9t2 + 4) dt 3. S (x2 + 2x + 1) dx 4. S ( V x+ 2Vx) 5 . S (4-3x2+5) dx 6. S (5 cos x + 4 sin x) dx x4