Since my idea of arts festvial integrates training students' artistic ability with improving their asthetic taste, I believe it will go a long way in art education, which is also the ultimate aim of university arts festival. 

由于我的艺术节思想把培养学生的艺术能力与提高学生的审美情趣结合起来，我相信这将对艺术教育有很大的帮助，这也是大学艺术节的最终目标。

解答如下：

integrate A with B 把A与B向结合

A和B可以是名词，也可以是动名词

integrate doing sth(1) with doing sth(2)

(1)doing sth(1)作动词integrate宾语

(2)doing sth(2)作介词with宾语

integrate training students' artistic ability with improving their asthetic taste,

(1)students' artistic ability 作动名词“training”宾语

(2)their asthetic taste作动名词“improving”的宾语

(3)training students' artistic ability为动名词短语作动词“integrate”宾语

(4)improving their asthetic taste为动名词短语作介词“with”的宾语

关于动名词语法功能讲解如下

(1)动名词具有动词语法功能：可以带有宾语和状语成分

Tom likes playing computer games.

computer games作动名词宾语

（动名词playing带有宾语说明动名词playing具有动词语法功能。）

She is afraid of going out alone at night.

 alone 和at night分别作动名词方式状语和时间状语

（动名词going out带有状语说明动名词具有动词语法功能。）

(2)动名词具有名词语法功能：可以放在动词后和介词后作宾语成分

Tom likes playing computer games.

playing computer games作谓语动词likes的宾语

（动名词playing computer games作谓语动词likes的宾语说明动名词具有名词法功能。）

She is afraid of going out alone at night.

going out alone at night作介词宾语

（动名词going out作介词of的宾语说明动名词具有名词法功能。）

(3)动名词具有形容词语法功能：可以放在名词前作定语说明名词功能和用途。

This is a swimming pool.

动名词作定语修饰后面名词pool，说明名词用途和功能

（动名词swimming作定语修饰后面名词pool，说明动名词具有形容词法功能。）