Ingerals + || = annoying...

[Aerith's Knight]

Absolute sign means sqrt(f(x)^2)

So it'll become:

F(x) = Int[ sqrt((x^2 - 4x + 3) (x^2 -4x + 3)) dx] 0-4

F(x) = Int[ sqrt( x^4 - 8x^3 + 22x^2 - 24x + 9) dx] 0-4

F(x) = (x^4 - 8x^3 + 22x^2 - 24x + 9)^1.5 * 1/1.5 * 1/(4x^3 - 24x^2 + 44x - 24) |0-4

F(0) = 9^1.5 * 1/1,5 * -1/24 = 9 * 3 * 2/3 * -1/24 = -18/24 = -3/4

F(4) = (0 + 9)^1.5 * 1/1.5 * 1/(24) = 3/4

F(4) - F(0) = 3/4 - (-3/4) = 1.5

...Necro's way might be easier, and less prone to mistakes