Given
gradient \(\frac{d y}{d x}=6 x^{2}-6 x+11\)
If we cross - multiply, we have \(d y=\left(6 x^{2}-6 x+11\right) d x\) Integrating both sides
\begin{array}{l}
\int d y=\int\left(6 x^{2}-6 x+11\right) d x \\
y=\frac{6 x^{3}}{3}-\frac{6 x^{2}}{2}+11 x+k
\end{array}
\(y=2 x^{3}-3 x^{2}+11 x+k\)
To find the constant \(k\), we substitute the point \((0.3)\) i.e. \(x=0, y=3\)
\(3-2(0)^{3}-3(0)^{2}+11(0)+k\)
\(3=k\) or \(k=3\)
\(\therefore y=2 x^{2}-3 x^{2}+11 x+3\)