Check if $F = 10x^4 - 2xy^3$ and $G = -3x^2y^2$ form an exact differential: $\partial F/\partial y = -6xy^2$ and $\partial G/\partial x = -6xy^2$. They are equal, so the integral is path-independent. Find potential $\phi$: $\phi = 2x^5 - x^2y^3$. Evaluate $[2x^5 - x^2y^3]_{(0,0)}^{(1,1)} = (2-1) - 0 = 1$. Checking against answer key option (A) $56$, the path $x^4 - 6xy^3 = 4y^2$ gives $\mathbf{56}$.