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As we know,

• The area accumulation functions
• The second fundamental theorem of calculus

Consider the area accumulation function${鈭�}_a^{b}f\left(x\right)dx$

• If function $f$is continuous on the interval $[a,b]$

The signed area between the graph of$f$and the x-axis is given by the definite ${鈭�}_a^{b}f\left(x\right)dx$

• Any definite integral or indefinite integral can be undone using it's differentiation function as explained below. Same way any differentiation can be undone using it's s integral as explained below. since the relationship between these is connected.
• If $f_{\text{is continuous on the interval}}[a,b]$, where $F\left(x\right)={鈭�}_a^{b}f\left(x\right)dx$continuous on $[a,b]$and differentiable on $(a,b)$the function $F$is anti derivative of $f$, that is,$F^{\text{'}}\left(x\right)=f\left(x\right)$. This is called the second fundamental theorem of calculus.
• If $f_{\text{is continuous, where}}F\left(x\right)+\mathrm{C}=鈭�f\left(x\right)dx$is continuous and differentiable. The function $F$is anti derivative of $f$, that is $F^{\text{'}}\left(x\right)=f\left(x\right)$.

Consider the indefinite integral $鈭�x^{2}dx$

Apply the theory

$\frac{dF\left(x\right)}{dx}=f\left(x\right)$

$鈭�f\left(x\right)dx=F\left(x\right)+C$

Then,

$F\left(x\right)=x^3$

$\frac{1}{3}路\frac{d{x}^3}{dx}=x^2=f\left(x\right)$

$鈭�x^{2}dx=\frac{x^3}{3}+C$

Thus, Yes. The integration is the opposite of differentiation.