To find the work done by the force when the body is displaced from $$x = 2 \, \mathrm{m}$$ to $$x = 4 \, \mathrm{m}$$, we use the formula for work done by a variable force in one dimension, which is the integral of the force with respect to displacement:

$$ W = \int_{x_1}^{x_2} F \, dx $$

Given the force $$F(x) = (3x^2 + 2x - 5) \, \mathrm{N}$$ and the limits of integration from $$x = 2 \, \mathrm{m}$$ to $$x = 4 \, \mathrm{m}$$, we can substitute these values into the equation:

$$ W = \int_{2}^{4} (3x^2 + 2x - 5) \, dx $$

Calculating the integral, we get:

$$ W = \left[\frac{3x^3}{3} + \frac{2x^2}{2} - 5x\right]_2^4 $$

This simplifies to:

$$ W = \left[x^3 + x^2 - 5x\right]_2^4 $$

Substituting the upper limit ($$x = 4$$) and then the lower limit ($$x = 2$$) into the antiderivative, and subtracting the latter from the former, we get:

$$ W = \left[(4)^3 + (4)^2 - 5(4)\right] - \left[(2)^3 + (2)^2 - 5(2)\right] $$

$$ W = (64 + 16 - 20) - (8 + 4 - 10) $$

$$ W = 60 - 2 $$

$$ W = 58 \, \mathrm{J} $$

Therefore, the work done by the force as the body displaces from $$x = 2 \, \mathrm{m}$$ to $$x = 4 \, \mathrm{m}$$ is $$58 \, \mathrm{J}$$.