I would say that learning "problem solving" is more important than learning how to type a formula into integrals.wolfram.com (which you should certainly use if you have an actual applied problem). Plus, if you want to go on to multivariable calculus you will need to understand the principles rather than just being able to get an answer to an integration.
I agree that calculus seems too "magical". But we should solve that by explaining more of the intuition and heuristics behind solving calculus problems, rather than teaching people to solve problems by brute force.
Guys, stop downvoting posts just because you disagree with them. If you have something to add to the discussion, add it. Parent was not abusive or off-topic or otherwise deserving of downmodding.
I agree that calculus seems too "magical". But we should solve that by explaining more of the intuition and heuristics behind solving calculus problems, rather than teaching people to solve problems by brute force.