Here are the given math problems from the image:

1. Find $f(x)$ given that $f'(x) = 6x + 1$ and $f(2) = 13$.
2. Find the equation of the curve $y = f(x)$ given that the gradient at any point $(x,y)$ is $\frac{dy}{dx} = 6x^2 - 2x$ and the curve passes through $(1,4)$.
3. If $y = 5x - 6$, determine the equation of the curve passing through $(2,-1)$.
4. Given $f'(x) = x^2 - 5$ and $f(2) = 3$, find $f(3)$.
5. If $F'(x) = ax^2 + 2x - 2$, the second derivative $F(x)$, and $F(1) - F(-2) = 0$, determine the function $F(x)$.

Would you like detailed solutions for all problems, or do you want to start with a specific one?

Here are five related questions to deepen understanding:

1. How do you find a function from its derivative using integration?
2. What is the role of initial conditions in solving integration problems?
3. How do you determine the equation of a curve given a gradient function?
4. What is the difference between first and second derivatives in a function?
5. How can definite integrals help solve problems involving function differences?

Tip: When solving for a function from its derivative, always include the constant of integration and use given conditions to find its value.