∫(2 to 3) (x^3) dx = [x^4/4] from 2 to 3 = (81/4 - 16/4) = 65/4 = 16.25.

∫(2 to 5) (4x - 1) dx = [2x^2 - x] from 2 to 5 = (50 - 5) - (8 - 2) = 40.

∫(0 to 1) (1 - x^2) dx = [x - x^3/3] from 0 to 1 = (1 - 1/3) = 2/3.

∫(0 to π) sin(x) dx = [-cos(x)] from 0 to π = -(-1 - 1) = 2.

∫(1 to 2) (3x^2 - 4) dx = [x^3 - 4x] from 1 to 2 = (8 - 8) - (1 - 4) = 3.

∫(1 to 3) (3x^2 - 2) dx = [x^3 - 2x] from 1 to 3 = (27 - 6) - (1 - 2) = 20.

∫(1 to 4) (2x + 1) dx = [x^2 + x] from 1 to 4 = (16 + 4) - (1 + 1) = 18.

∫(2 to 3) (x^3 - 3x^2 + 2) dx = [x^4/4 - x^3 + 2x] from 2 to 3 = (81/4 - 27 + 6) - (16/4 - 8 + 4) = 1.

The integral of (2x + 3) is (2x^2/2) + 3x + C = x^2 + 3x + C.

The integral of (x^2 - 2x + 1) is (1/3)x^3 - x^2 + x + C.

∫(0 to 1) (x^2 + 2x) dx = [x^3/3 + x^2] from 0 to 1 = (1/3 + 1) - (0) = 4/3.

∫(0 to 2) (x^2 + 1) dx = [x^3/3 + x] from 0 to 2 = (8/3 + 2) - (0) = 4.

∫(0 to π) sin(x) dx = [-cos(x)] from 0 to π = [1 - (-1)] = 2.

∫(1 to 3) (x^2 - 2x + 1) dx = [(x^3/3 - x^2 + x)] from 1 to 3 = (9/3 - 9 + 3) - (1/3 - 1 + 1) = 0.

∫(1 to 4) (x^3) dx = [x^4/4] from 1 to 4 = (256/4 - 1/4) = 63.

The indefinite integral of e^x is e^x + C.

The integral of x^n dx is (x^(n+1))/(n+1) + C.