Looking at etymology
early 13c., "skill as a result of learning or practice," from O.Fr. art (10c.), from L. artem (nom. ars) "work of art; practical skill; a business, craft," from PIE *ar-ti- (cf. Skt. rtih "manner, mode;" Gk. arti "just," artios "complete, suitable," artizein "to prepare;" L. artus "joint;" Armenian arnam "make;" Ger. art "manner, mode"), from base *ar- "fit together, join" (see arm (1)). In M.E. usually with sense of "skill in scholarship and learning" (c.1300), especially in the seven sciences, or liberal arts. This sense remains in Bachelor of Arts, etc. Meaning "human workmanship" (as opposed to nature) is from late 14c. Sense of "cunning and trickery" first attested c.1600. Meaning "skill in creative arts" is first recorded 1610s; especially of painting, sculpture, etc., from 1660s. Broader sense of the word remains in artless.
Fine arts, "those which appeal to the mind and the imagination" first recorded 1767. Expression art for art's sake (1836) translates Fr. l'art pour l'art. First record of art critic is from 1865. Arts and crafts "decorative design and handcraft" first attested in the Arts and Crafts Exhibition Society, founded in London, 1888.
Shows how the meanings evolved from a wider meaning into a more narrow one. In context of Bachelor of Arts, it is obvious that it refers to "skill in scholarship and learning".
Today when we talk about artist and art the immediate association are paintings, sculptures and other "works to be appreciated primarily for their beauty or emotional power".
However some connotations from older meanings still remain:
- in the expression "art of making something" we don't refer to l'art pur l'art, but we refer to craftsmanship (an older meaning)
- in slightly metaphorical sense, "art of..." can be taken to mean skill, as in art of persuasion, art of motorcycle maintenance (wikipedia), art of war, rather then art that is normally exhibited in a gallery
- in "college of arts and sciences", arts refer to "studies intended to provide general knowledge and intellectual skills"
- in artless, the 1st meaning lists: "lacking art, knowledge, or skill", extending the semantic to include knowledge and skills in what should be a direct antonym
Also, from wikipedia on the arts
In the Middle Ages, Artes Liberales (liberal arts) taught in medieval universities as part of the Trivium: (grammar, rhetoric, and logic) and the Quadrivium (arithmetic, geometry, music, and astronomy), and the Artes Mechanicae (mechanical arts) such as metalworking, farming, cooking, business and the making of clothes or cloth. The modern distinctions between "artistic" and non-artistic skills did not develop until the Renaissance.
I think it is reasonable to assume that such usage as in the above influenced etymologies of many other terms and I think it is easy to justify, even today, usage that when talking about arts encompasses skill and craftsmanship.
As for capitalized the Art - you will find it referring to almost anything; for more colorful examples see magic, alchemy and so on. Actually any kind of human activity can be called "art of..", and especially in the writings it is often the most appropriate word to describe studies of such interests. In those cases practitioners usually refer to their subject simply, and sometimes deliberately cryptic, as the Art.