please help with questions shown.

In Exercises I through 30, find the indicated integral. Check your answers by differentiation. 21. ( 8 3 - 2x 3) ( 1 - 5 ) dx 23. Vi(2 - 1) dt Vitex / 2 ) dy In Exercises 31 through 34, solve the given initial value problem for y = f(x). 31. dx dy = 3x - 2 where y = 2 when x = -1 dy 1 33. : 2. dx where y = -1 when x = 1 X * 2In Exercises 35 through 42, the slope f'(x) at each point (x, y) on a curve y = f(x) is given along with a particular point (a, b) on the curve. Use this information to find f(x). 35. f'(x) = 4x + 1; (1, 2) 37. f'(x) = -x(x + 1); (-1, 5) 39. f'(x) = x3 - 2 + 2; (1, 3) 41. f'(x) = e-* + x; (0, 4)