From The Annals of Imperial Rome, by Tacitus (ca 56 to 117 AD) writing sometime in the late first or early second century AD:

"But neither human resources, nor imperial munificence, nor appeasement of the gods, eliminated sinister suspicions that the fire had been instigated. To suppress this rumor, Nero fabricated scapegoats-and punished with every refinement the notoriously depraved Christians (as they were popularly called). Their originator, Christ, had been executed in Tiberius' reign by the governor of Judea, Pontius Pilate. But in spite of this temporary setback the deadly superstition had broken out afresh, not only in Judea (where the mischief had started) but even in Rome. All degraded and shameful practices collect and flourish in the capital.

"First, Nero had self-acknowledged Christians arrested. Then, on their information, large numbers of others were condemned - not so much for incendiarism as for their anti-social tendencies. Their deaths were made farcical. Dressed in wild animals skins, they were torn to pieces by dogs, or crucified, or made into torches to be ignited after dark as substitutes for daylight. Nero provided his Gardens for the spectacle, and exhibited displays in the Circus, at which he mingled with the crowd - or stood in a chariot, dressed as a charioteer. Despite their guilt as Christians, and the ruthless punishment it deserved, the victims were pitied. For it was felt that they were being sacrificed to one man's brutality rather than to the national interest."

From Antiquities of the Jews by Flavius Josephus - writing sometime in the late first century.

"About this time there lived Jesus, a wise man, if indeed one ought to call him a man. For he was one who performed surprising deeds and was a teacher of such people as accept the truth gladly. He won over many Jews and many of the Greeks. He was the Christ. And when, upon the accusation of the principal men among us, Pilate had condemned him to a cross, those who had first come to love him did not cease. He appeared to them spending a third day restored to life, for the prophets of God had foretold these things and a thousand other marvels about him. And the tribe of the Christians, so called after him, has still to this day not disappeared."

That's because Islam wants the Anti-Christ in many branches and so it lies in order to bring that about.

I believe the only trusted source of information about Jesus is the Bible.

Well, according to the bible, he died crucified, I don't know what the Koran says about that, but the truth is that Jesus had a mission, which was to spread the word of God, and in a way he achieved it, no matter how he died.

The canonical Christian teaching is that He truly died. Or at least His body did, while His soul "descended to Hell" where He proclaimed victory over sin and Death itself (search for "Harrowing of Hell" for details, however little is actually said about it in the Bible itself).

(Some interpretations believe that through this act he also "opened the Heavens" and liberated all the righteous that died before him.)

He then resurrected Himself (being part of the Divine Trinity and all) as a divine act (further demonstrating His dominance over Death), and eventually ascended into Heaven, body and soul, but that, I believe, is out of scope of your question.

TL;DR: Canonical Christian belief is that Jesus really died by crucifiction, entered afterlife, defeated Death, resurrected Himself, thus completing His mission.