Infinitive : - In grammar , the infinitive is the form of a verb that has no inflection to indicate person , number , mood or tense . By far , the most common form of an infinitive in English language is with the particle ' to ' , such as ' to walk ' ' to cry ' etc . This is known as ' to - infinitive ' . It can function as a subject , direct object , subject complement , adjective , or adverb in a sentence .

Forget Plus Gerund:

Forgot + Gerund : Point to the past. It has the meaning of recollection.

When forget, regret and remember are followed by a gerund, the gerund refers to an action that happened earlier than the main verb. The gerund could be replaced by the present perfect participle in these sentences to make the sequence of events more explicit. Forget is frequently used with never in the simple future form.

Example:

• I forgot posting the letter.

In the question : -

1. Don’t ______________  call the agency.  you need to call the agency .

In this sentence , the correct infinitive that can be  placed in the blank part is forgot to as it followed by an infinitive for something that you need or needed to do, that has or had to be done.

2. He ____________ an application.

In this sentence , the correct infinitive that can be  placed in the blank part is forgot to as it refers to an action happening at the same time of the main verb, or later.

Thus , the Correct Option is D , which is 1. Forgot to 2. Forgot writing .

Infinitive : - In grammar , the infinitive is the form of a verb that has no inflection to indicate person , number , mood or tense . By far , the most common form of an infinitive in English language is with the particle ' to ' , such as ' to walk ' ' to cry ' etc . This is known as ' to - infinitive ' . It can function as a subject , direct object , subject complement , adjective , or adverb in a sentence .

Forget Plus Gerund:

Forgot + Gerund : Point to the past. It has the meaning of recollection.

When forget, regret and remember are followed by a gerund, the gerund refers to an action that happened earlier than the main verb. The gerund could be replaced by the present perfect participle in these sentences to make the sequence of events more explicit. Forget is frequently used with never in the simple future form.

Example:

• I forgot posting the letter.

In the question : -

I will never ______________ across Europe.  In this sentence , the correct infinitive that can be  placed in the blank part is forgot and gerund form travelling as it refers to something that has happened .

Thus , the Correct Option is C , which is Forgot Travelling .

Infinitive : - In grammar , the infinitive is the form of a verb that has no inflection to indicate person , number , mood or tense . By far , the most common form of an infinitive in English language is with the particle ' to ' , such as ' to walk ' ' to cry ' etc . This is known as ' to - infinitive ' . It can function as a subject , direct object , subject complement , adjective , or adverb in a sentence .

Forget Plus Gerund:

Forgot + Gerund : Point to the past. It has the meaning of recollection.

When forget, regret and remember are followed by a gerund, the gerund refers to an action that happened earlier than the main verb. The gerund could be replaced by the present perfect participle in these sentences to make the sequence of events more explicit. Forget is frequently used with never in the simple future form.

Example:

• I forgot posting the letter.

In the question : -

1. He __________ do his homework.

In this sentence , the correct infinitive that can be  placed in the blank part is forgot to as it refers to do something is to not remember something that you needed to do .

2. He ____________ to Spain. 

In this sentence , the correct infinitive that can be  placed in the blank part is forgot and the gerund form of go which is going as it refers to something is to have no memory of something you have done .

Thus , the Correct Option is C , which is 1. Forgot to 2. Forgot going .