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How can we derive FM from PM?

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How can we derive FM from PM?

(a) by integrating the modulating signal before applying to the PM oscillator

(b) by integrating signal out of the PM oscillator

(c) by differentiating the modulating signal before applying to the PM oscillator

(d) by differentiating signal out of the PM oscillator

The question was posed to me during an online interview.

I would like to ask this question from Switching Circuit topic in chapter Side Band Techniques of Analog Communications

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The correct answer is (a) by integrating the modulating signal before applying to the PM oscillator

To explain: Frequency modulation can be derived from phase modulated system, if we integrate our modulating signal before applying our wave to PM oscillator. Likewise, Phase modulation can be obtained from frequency modulated system, if we differentiate our modulating signal before applying our wave to FM oscillator.

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