Claim: Yanukovych aimed for balanced ties with West & Russia, staying neutral; he never pledged EU economic integration.
This is mostly true.
Yanukovych attempted to balance between Western and Russian powers, however it cannot be said that he never wanted to economically integrate into the West.
At the start of Yanukovch's governance, according to a BBC article from 2010, he stated "I remain committed to a balanced policy, which will protect our national interests both on our easter border- I mean with Russia- and of course with the European Union".
His actions seem to reflect this sentiment, with preference to Russia in certain moments and preference to the West in others. His first policy priority, according to brookings.edu, was to improve relations with Moscow (there had been a recent falling out when former leader Victor Yushchenko bid to join NATO and began leaning towards other Western ideals). So Yanukovch was more lenient with Russia, allowing its Black Sea Fleet to stay in Crimea and stopping the bid to join NATO.
However, Yanukovch flip-flopped back to the West when Putin made threatening comments about a "greater Eurasia". Critically, Yanukovch pursued a free trade agreement 2011 with EU, which renders the second part of the claim above erroneous. However, once Russia made it clear they would sanction Ukraine with poor trade, Yanukovch again flip-flopped back to align with Russian interests.
In 2013, according to a different BBC article from the same year, Yanukovych rejected the EU association agreement, which led to mass protests in Ukraine. Russia and the EU both accused the other of being too controlling, while Ukraine stayed tied and balanced in the middle. Yanukovych wanted the benefits of democracy and protection from West. However, he also wanted trade benefits and respect from Russia.
Therefore, Yanukovych's balance between the two achieved multiple goals, and he did do this as Ukraine stayed mostly between the two underneath his rule.
However, in part of the flip-flop process involved in Yanukovych's balancing act there were moments in which Yanukovych, if not pledging, was leaning toward UN economic tendencies, if not full integration.
Note: the BBC is a Western newspaper which can reflect Western bias. However, the information I got from the articles seems mostly unbiased and both were written before the Ukraine War and even the annexation of Crimea, which led to more division and distinction in West/Russian bias.
http://news.bbc.co.uk/1/hi/world/europe/4038803.stm
https://www.brookings.edu/articles/ukraine-balancing-russia-the-west-and-democracy/
https://www.bbc.com/news/world-europe-25162563
