Question: How is Kashmir legally claimed by India?
About the article "Pakistan", section "Kashmir conflict".

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120,849 km2.
of area that is claimed by India and administered by Pakistan and China. 
The northernmost point that India claims lies in territory now administered by China as part of Xinjiang but once claimed by Hunza and therefore claimed by India as part of the disputed state of Kashmir.
The northernmost point administered by India lies in Kashmir.
India's claim to the whole of Kashmir is disputed by Pakistan and China, with the territory currently partitioned into Pakistan's states of Azad Kashmir and Gilgit-Baltistan, the Chinese region of Aksai Chin and the Indian-administered state of Jammu and Kashmir.
This list provides the northernmost point as claimed by India; the northern-most disputed point that is administered by India; and the northern-most undisputed point in India.
This case also applies to the highest elevated regions.
India's eastern-most state is Arunachal Pradesh.
Part of the state is claimed by China as "South Tibet", though administered by India, The easternmost of Indian-administered territory is located in this disputed region.
Consequently, this list mentions both the disputed and undisputed eastern-most points in India. 
  Kashmir valley, surrounded by Pir Panjal mountain ranges, between Pakistan, India and Ladakh.
It is one of the 3 divisions of the Indian-administered state of Jammu and Kashmir.
Kashmir and Jammu (princely state), the former princely state which came to an end in 1947.
The Kashmir Conflict, the territorial dispute over the Kashmir region: * Jammu and Kashmir, area of Kashmir administered by Republic of India as a state; disputed by Pakistan.
* Azad Jammu and Kashmir, areas of the Kashmir region administered by Pakistan; disputed by India.
* Trans-Karakoram Tract, an area ceded by Pakistan to China by the Sino-Pak Border Agreement in 1963; disputed by India.
* Aksai Chin, an area of disputed Kashmir region administered by China; disputed by India.  
Kashmir Shaivism: Kashmir Saivism, a householder religion, was based on a strong monistic interpretation of the "Bhairava Tantras" (and its subcategory the "Kaula Tantras"), which were tantras written by the Kapalikas.
There was additionally a revelation of the "Siva Sutras" to Vasugupta.
Kashmir Saivism claimed to supersede the dualistic Shaiva Siddhanta.
Somananda, the first theologian of monistic Saivism, was the teacher of Utpaladeva, who was the grand-teacher of Abhinavagupta, who in turn was the teacher of Ksemaraja.
The label Kashmir Shaivism, though unfortunately now widely adopted, is really a misnomer, for it is clear that the dualistic Shaiva Siddhanta was "also" in North India at one point in time.  
  India claims Aksai Chin and Trans-Karakoram Tract, as part of Jammu and Kashmir.
China claims most of Arunachal Pradesh, a contested disputed territory of north-east India by not recognising the McMahon Line.
People's Republic of China.
Two regions are claimed by both India and China.
Aksai Chin is in the disputed territory of Kashmir, at the junction of India, Tibet and Azad Kashmir.
India claims the 38,000-square-kilometre territory, currently administered by China.
India also considers the cessation of Shaksam Valley to China by Pakistan as illegal and a part of its territory.
Arunachal Pradesh is a state of India in the country's northeast, bordering on Bhutan, Burma and China.
Though it is under Indian administration, China calls the 90,000-square-kilometre area as South Tibet.
Also the boundary between the North Indian states of Himachal Pradesh and Uttarakhand with China's Tibet is not properly demarcated with some portions under de facto administration of India.