Solve y = ∫ x^2 wrt x-C

$$y = \int x ^ { 2 } d x - C$$

Solve for C

$$C=\frac{x^{3}-3y+С}{3}$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$\int x^{2}\mathrm{d}x-C=y$$

Subtract \int x^{2}\mathrm{d}x from both sides.

$$-C=y-\int x^{2}\mathrm{d}x$$

The equation is in standard form.

$$-C=-\frac{x^{3}}{3}+y-С$$

Divide both sides by -1.

$$\frac{-C}{-1}=\frac{-\frac{x^{3}}{3}+y-С}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$C=\frac{-\frac{x^{3}}{3}+y-С}{-1}$$

Divide y-\frac{x^{3}}{3}-С by -1.

$$C=\frac{x^{3}}{3}-y+С$$

Solve for y

$$y=\frac{x^{3}}{3}-C+С$$