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The image you provided appears to be a handwritten mathematical question. Here's a transcription of the visible text, although some parts are unclear due to the quality of the image:

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"If the fundamental equation of calculus involving an integral is:

\[ f(b) - f(a) = \int_a^b f'(x) \, dx \]

then, state:
(a) Which part of the equation above is primarily involved with the concept of the derivative (rate of change)?
(b) Which part involves an integral (accumulation of values)?
(c) Continuity condition on \( f(x) \)?

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Let the function \( f(x) \) be continuous and differentiable, with initial conditions as follows:
\[ f'(x) = \sin(x) \]
\[ f(0) = 1, \]
\[ f(\pi) = 0. \]"

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Would you like a detailed explanation or solution to this problem? I can also address specific sections like the derivative, integral, or initial conditions.

### Related Questions:
1. What is the Fundamental Theorem of Calculus?
2. How does the derivative relate to the concept of rate of change?
3. What is the geometric interpretation of an integral?
4. Why is continuity important for the Fundamental Theorem of Calculus?
5. How do initial conditions affect the solution of a differential equation?

**Tip:** When solving integral problems, breaking down the components of the Fundamental Theorem of Calculus helps to better understand the connection between differentiation and integration.

This problem covers the Fundamental Theorem of Calculus, focusing on derivatives, integrals, and continuity. It includes an integral equation and an initial condition-based differential equation with the function f(x). Suitable for advanced high school or college-level calculus students.

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