Differentiating is the process by which when ${\displaystyle y}$ is given us (as a function of ${\displaystyle x}$), we can find ${\displaystyle {\frac {dy}{dx}}}$.

Like every other mathematical operation, the process of differentiation may be reversed; thus, if differentiating ${\displaystyle y=x^{4}}$ gives us ${\displaystyle {\frac {dy}{dx}}=4x^{3}}$; if one begins with ${\displaystyle {\frac {dy}{dx}}=4x^{3}}$ one would say that reversing the process would yield ${\displaystyle y=x^{4}}$. But here comes in a curious point. We should get ${\displaystyle {\frac {dy}{dx}}=4x^{3}}$ if we had begun with any of the following: ${\displaystyle x^{4}}$, or ${\displaystyle x^{4}+a}$, or ${\displaystyle x^{4}+c}$, or ${\displaystyle x^{4}}$ with any added constant. So it is clear that in working backwards from ${\displaystyle {\frac {dy}{dx}}}$ to ${\displaystyle y}$, one must make provision for the possibility of there being an added constant, the value of which will be undetermined